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All questions of Time and Work for SSC CGL Exam
A can type 100 letters in 5 minutes. B and C typing together can type 50 letters in 2 minutes. If all of them working together then can type 90 letters in how many minutes?- a)2 minutes
- b)4 minutes
- c)5 minutes
- d)10 minutes
- e)None
Correct answer is option 'A'. Can you explain this answer?
A can type 100 letters in 5 minutes. B and C typing together can type 50 letters in 2 minutes. If all of them working together then can type 90 letters in how many minutes?
a)
2 minutes
b)
4 minutes
c)
5 minutes
d)
10 minutes
e)
None
 | Aisha Gupta answered |
(1/5+1/4)
20/9*90/100 = 2
20/9*90/100 = 2
A can do a piece of work in 21days. B is 50% more efficient than A. C is twice efficient than B. A started the work alone and worked for some days and left the work then B and C joined together and completed the work in 2 days. Then how many days does A worked alone?- a)7 Days
- b)12 Days
- c)14 Days
- d)21 Days
- e)None
Correct answer is option 'B'. Can you explain this answer?
A can do a piece of work in 21days. B is 50% more efficient than A. C is twice efficient than B. A started the work alone and worked for some days and left the work then B and C joined together and completed the work in 2 days. Then how many days does A worked alone?
a)
7 Days
b)
12 Days
c)
14 Days
d)
21 Days
e)
None
 | Machine Experts answered |
A = 21 B = 14 C =7
x/21+2*(1/14+1/7) = 1
x = 12.
x/21+2*(1/14+1/7) = 1
x = 12.
7 Indian and 4 American finish a job in 6 days. 7 African and 3 American finish the same job in 8 days. The efficiency of each person of a particular nationality is same but different from others. One Indian One American and One African will complete the work in:- a)10 days
- b)12 days
- c)24 days
- d)36 days
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
7 Indian and 4 American finish a job in 6 days. 7 African and 3 American finish the same job in 8 days. The efficiency of each person of a particular nationality is same but different from others. One Indian One American and One African will complete the work in:
a)
10 days
b)
12 days
c)
24 days
d)
36 days
e)
None of these
| | Anaya Patel answered |
7I + 4Am = 1/6
7Af + 4Am = 1/8
7I + 7Af + 7Am = 7/24
1I + 1Af + 1Am = 1/24
One Indian One American and One African will complete the work in – 24 days.
7Af + 4Am = 1/8
7I + 7Af + 7Am = 7/24
1I + 1Af + 1Am = 1/24
One Indian One American and One African will complete the work in – 24 days.
Arun can do a piece of work in 40 days, but Bala can do the same work in 5 days less, than Arun, when working alone. Arun and Bala both started the work together but Bala left after some days and Arun finished the remaining work in 30 days with half of his efficiency but he did the work with Bala with his complete efficiency. For how many days they had worked together?- a)25/3 days
- b)31/3 days
- c)35/3 days
- d)38/3 days
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Arun can do a piece of work in 40 days, but Bala can do the same work in 5 days less, than Arun, when working alone. Arun and Bala both started the work together but Bala left after some days and Arun finished the remaining work in 30 days with half of his efficiency but he did the work with Bala with his complete efficiency. For how many days they had worked together?
a)
25/3 days
b)
31/3 days
c)
35/3 days
d)
38/3 days
e)
None of these
| | Anaya Patel answered |
1 day work of Arun and Bala = 1/40 + 1/35 = 15/280
Arun finished the remaining work in 30 days = 30 * 1/40 * 2 = 3/8
Remaining work done by Arun and Bala = 5/8
Worked together = (5/8)/(15/280) = 35/3 days.
Arun finished the remaining work in 30 days = 30 * 1/40 * 2 = 3/8
Remaining work done by Arun and Bala = 5/8
Worked together = (5/8)/(15/280) = 35/3 days.
A and B together can do a piece of work in 24 days, which B and C together can do it in 32 days. After A has been working at it for 10 days and B for 14 days, C finishes it in 26 days. In how many days C alone will do the work?- a)32
- b)36
- c)44
- d)48
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
A and B together can do a piece of work in 24 days, which B and C together can do it in 32 days. After A has been working at it for 10 days and B for 14 days, C finishes it in 26 days. In how many days C alone will do the work?
a)
32
b)
36
c)
44
d)
48
e)
None of these
| | Anaya Patel answered |
Correct Answer :- d
Explanation : Work done by (A+B)'s in 1 day = 24
work done by (B+C)'s in 1 day = 32
Let C does a work in x days
Then work done by C in a day = 1/x
According to the question
A's 10 day's work + B's 14 day's work + C's 26 day's work = 1
10A + 14B + 26C = 1 ;
10A + 10B + 4B + 4C + 22C = 1 ;
10(A + B ) + 4( B + C ) + 22C = 1 ;
10( 1/24 ) + 4( 1/32 ) + 22C = 1 ;
10/24 + 4/32 + 22C = 1 ;
13/24 + 22C = 1 ;
22C = 1 - 13/24 ;
22C = 11/24 ;
2C = 1/24 ;
C = 1/48 ;
Therefore , C alone takes 48 days to finish the job.
A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.- a)32 minutes
- b)20 minutes
- c)25 minutes
- d)40 minutes
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.
a)
32 minutes
b)
20 minutes
c)
25 minutes
d)
40 minutes
e)
None of these
 | Preeti Khanna answered |
2000 nuts are produced in 14 minutes (10 minutes break and 500 nuts per minutes so 4 minutes to produce 2000 nuts ), for next 2000 nuts it will take 14 minutes more, and for more two thousand it will take 4 minutes more, so total time = 32 minutes
similarly, 6000 bolts are produced in 20 + 5 = 25 minutes
so minimum time required is 32 minutes
similarly, 6000 bolts are produced in 20 + 5 = 25 minutes
so minimum time required is 32 minutes
Sekar, Pradeep and Sandeep can do a piece of work in 15 days. After all the three worked for 2 days, sekar left. Pradeep and Sandeep worked for 10 more days and Pradeep left. Sandeep worked for another 40 days and completed the work. In how many days can sekar alone complete the work if sandeep can complete it in 75 days?- a)25 days
- b)20 days
- c)30 days
- d)35 days
- e)15 days
Correct answer is option 'C'. Can you explain this answer?
Sekar, Pradeep and Sandeep can do a piece of work in 15 days. After all the three worked for 2 days, sekar left. Pradeep and Sandeep worked for 10 more days and Pradeep left. Sandeep worked for another 40 days and completed the work. In how many days can sekar alone complete the work if sandeep can complete it in 75 days?
a)
25 days
b)
20 days
c)
30 days
d)
35 days
e)
15 days
 | Bank Exams India answered |
Assume the total work to be 600 units. (LCM of all the numbers) Then Sandeep’s 1 day work = 8 units.
All three’s 1 day work = 40 units.All work together in the first 2 days
Work done in the first 2 days = 40 × 2 = 80 units
Sandeep alone works during the last 40 days
Work done in the last 40 days = 40 × 8 = 320 units
Remaining work = 600 – (320 + 80) = 200 units
This work is done by pradeep and sandeep in 10 days.
Pradeep and Sandeep together’s 1 day work = 20 units
Sekar’s 1 day work = All three 1 day work – Pradeep and Sandeep together’s 1 day
work = 40 units – 20 units = 20 units
Sekar can do the work of 600 units in 30 days.
All three’s 1 day work = 40 units.All work together in the first 2 days
Work done in the first 2 days = 40 × 2 = 80 units
Sandeep alone works during the last 40 days
Work done in the last 40 days = 40 × 8 = 320 units
Remaining work = 600 – (320 + 80) = 200 units
This work is done by pradeep and sandeep in 10 days.
Pradeep and Sandeep together’s 1 day work = 20 units
Sekar’s 1 day work = All three 1 day work – Pradeep and Sandeep together’s 1 day
work = 40 units – 20 units = 20 units
Sekar can do the work of 600 units in 30 days.
If P and Q work together, they will complete a job in 7.5 days. However, if P works alone and completes half the job and then Q takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will Q alone take to do the job if P is more efficient than Q?- a)20 days
- b)30 days
- c)40 days
- d)10 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
If P and Q work together, they will complete a job in 7.5 days. However, if P works alone and completes half the job and then Q takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will Q alone take to do the job if P is more efficient than Q?
a)
20 days
b)
30 days
c)
40 days
d)
10 days
e)
None of these
 | Naroj Boda answered |
1/P + 1/Q = 2/15 from first line. Now, let P take x days and Q takes y days to complete half the work respectively.
x/P = 1/2, x = P/2 similarly y/Q = 1/2, y = Q/2
so, x +y = 20 i.e. P/2 + Q/2 = 20, P +Q = 40
solve both equation, u will get Q = 30 days
x/P = 1/2, x = P/2 similarly y/Q = 1/2, y = Q/2
so, x +y = 20 i.e. P/2 + Q/2 = 20, P +Q = 40
solve both equation, u will get Q = 30 days
Arun can do a certain work in the same time in which Bipasha and Rahul together can do it. If Arun and Bipasha together could do it in 10 days and Rahul alone in 50 days, then Bipasha alone could do it in:- a)15 days
- b)20 days
- c)25 days
- d)30 days
- e)35 days
Correct answer is option 'C'. Can you explain this answer?
Arun can do a certain work in the same time in which Bipasha and Rahul together can do it. If Arun and Bipasha together could do it in 10 days and Rahul alone in 50 days, then Bipasha alone could do it in:
a)
15 days
b)
20 days
c)
25 days
d)
30 days
e)
35 days
 | Kavya Saxena answered |
Arun, Bipasha and rahul’s 1 day work = 1/10 + 1/50 = 6/50 = 3/25
Arun’s 1 day work = Bipasha + Rahul ‘s 1 day work
2*(Arun’s 1 day work) = 3/25
Arun’s 1 day work = 3/50
Bipasha’s 1 day work = 1/10 – 3/50 = 2/50 = 1/25
Arun’s 1 day work = Bipasha + Rahul ‘s 1 day work
2*(Arun’s 1 day work) = 3/25
Arun’s 1 day work = 3/50
Bipasha’s 1 day work = 1/10 – 3/50 = 2/50 = 1/25
A piece of work has to be completed in 50 days, a number of men are employed but it is found that only half of the work is done in 30 days, then an additional 20 men were joined to complete the work on time. How many men initially put to work?- a)30
- b)35
- c)40
- d)45
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
A piece of work has to be completed in 50 days, a number of men are employed but it is found that only half of the work is done in 30 days, then an additional 20 men were joined to complete the work on time. How many men initially put to work?
a)
30
b)
35
c)
40
d)
45
e)
None of these
 | KS Coaching Center answered |
suppose Initially X men get employed. Half work is done in 30 days it means full work will be done by X men in 60 days. Now,
Work done = 1/2 = [20*(x + 20)]/60X
X = 40
Work done = 1/2 = [20*(x + 20)]/60X
X = 40
The ratio of efficiency of Arun is to Chitra is 5:3. The ratio of number of days taken by Bala is to Chitra is 2:3. Arun takes 6 days less than Chitra, when Arun and Chitra complete the work individually. Bala and Chitra started the work and left after 2 days. The number of days taken by Arun to finish the remaining work is?- a)4 days
- b)5 days
- c)6 days
- d)9 days
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
The ratio of efficiency of Arun is to Chitra is 5:3. The ratio of number of days taken by Bala is to Chitra is 2:3. Arun takes 6 days less than Chitra, when Arun and Chitra complete the work individually. Bala and Chitra started the work and left after 2 days. The number of days taken by Arun to finish the remaining work is?
a)
4 days
b)
5 days
c)
6 days
d)
9 days
e)
None of these
| | KS Coaching Center answered |
Ratio of number of days = 9:10:15
Work done By B and C in first two days = 2*1/6 = 1/3
Rest of the work = 2/3
Number of days = (2/3)/(1/9) = 6 days
Work done By B and C in first two days = 2*1/6 = 1/3
Rest of the work = 2/3
Number of days = (2/3)/(1/9) = 6 days
A Contractor employed a certain number of workers to finish constructing a building in a certain scheduled time. Some time later, when a part of work had been completed, he realized that the work would get delayed by half of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the building on the scheduled time. How much work he had been completed, before increasing the number of workers?- a)200/3%
- b)100/3%
- c)300/3%
- d)Can’t be determined
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
A Contractor employed a certain number of workers to finish constructing a building in a certain scheduled time. Some time later, when a part of work had been completed, he realized that the work would get delayed by half of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the building on the scheduled time. How much work he had been completed, before increasing the number of workers?
a)
200/3%
b)
100/3%
c)
300/3%
d)
Can’t be determined
e)
None of these
| | KS Coaching Center answered |
D * x +(100- D) * 2x= 150x
⇒ D = 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
⇒ D = 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
Efficiency of A is 25% more then B and B takes 25 days to complete a piece of work. A started a work alone and then B joined her 5 days before actual completion of the work. For how many days A worked alone?- a)9
- b)11
- c)10
- d)25
- e)12
Correct answer is option 'B'. Can you explain this answer?
Efficiency of A is 25% more then B and B takes 25 days to complete a piece of work. A started a work alone and then B joined her 5 days before actual completion of the work. For how many days A worked alone?
a)
9
b)
11
c)
10
d)
25
e)
12
| | KS Coaching Center answered |
Efficiency (A : B) = 5 : 4
Number of days(A : B) = 4x : 5x = 4x : 25
∴ Number of days required by A to finish the work alone = 4x
= 4 x 5 = 20.
A and B work together for last 5 days = 5 x 9 = 45%
Efficiency of A = 5% and B’s efficiency = 4%
∴ No. of days taken by A to complete 55% work = 55/5 = 11days
Number of days(A : B) = 4x : 5x = 4x : 25
∴ Number of days required by A to finish the work alone = 4x
= 4 x 5 = 20.
A and B work together for last 5 days = 5 x 9 = 45%
Efficiency of A = 5% and B’s efficiency = 4%
∴ No. of days taken by A to complete 55% work = 55/5 = 11days
Among four persons Anuj, Bhim, Carl and Dinesh. Anuj takes thrice as much time as Bhim to complete a piece of work. Bhim takes thrice as much time as Carl and Carl takes thrice as much time as Dinesh to complete the same work. If all together they take 3 days to complete the work. Find the time taken by Bhim alone to complete the work alone.- a)20 days
- b)30 days
- c)40 days
- d)50 days
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Among four persons Anuj, Bhim, Carl and Dinesh. Anuj takes thrice as much time as Bhim to complete a piece of work. Bhim takes thrice as much time as Carl and Carl takes thrice as much time as Dinesh to complete the same work. If all together they take 3 days to complete the work. Find the time taken by Bhim alone to complete the work alone.
a)
20 days
b)
30 days
c)
40 days
d)
50 days
e)
None of these
 | Faizan Khan answered |
Let Bhim takes x days alone to complete the job, so Anuj will take 3x days, Carl will take x/3 days and Dinesh will take x/9 days to complete the work alone
1/3x + 1/x + 3/x + 9/x = 1/3
Solve for x
1/3x + 1/x + 3/x + 9/x = 1/3
Solve for x
If P can do 1/3 of the work in 5 days and Q can do 1/4 of the work in 6 days, then how much money will Q get if they were paid a total of 390 rupee?- a)120
- b)150
- c)170
- d)190
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
If P can do 1/3 of the work in 5 days and Q can do 1/4 of the work in 6 days, then how much money will Q get if they were paid a total of 390 rupee?
a)
120
b)
150
c)
170
d)
190
e)
None of these
| | Bank Exams India answered |
sol = P can alone complete the whole work in 15 days and Q can complete the same work alone in 24 days. So ratio of work done by them 1/15: 1/24 i.e. 8: 5
Q get = (5/13)*390 = 150
Q get = (5/13)*390 = 150
A piece of work is to be completed in 100days, 11 Men are employed to do the work it is found that after 50 days only 1/3 rd work is completed. Now additionally how many more Men are to be employed to work to finish the work in time?- a)5
- b)6
- c)7
- d)11
- e)None
Correct answer is option 'D'. Can you explain this answer?
A piece of work is to be completed in 100days, 11 Men are employed to do the work it is found that after 50 days only 1/3 rd work is completed. Now additionally how many more Men are to be employed to work to finish the work in time?
a)
5
b)
6
c)
7
d)
11
e)
None
| | Bank Exams India answered |
11*50/1/3 = (11+x)*50/2/3
X = 11
X = 11
A can do a piece of work in 60days working 14 hours. B has the same efficiency as of A. A and B started working together. A works 5,6,7 and 8 hours respectively on first four days and repeats the cycle again. Then B has to work how many hours daily if they together completed the work in 80 days?- a)1 Hour
- b)2 Hours
- c)3 Hours
- d)4 Hours
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
A can do a piece of work in 60days working 14 hours. B has the same efficiency as of A. A and B started working together. A works 5,6,7 and 8 hours respectively on first four days and repeats the cycle again. Then B has to work how many hours daily if they together completed the work in 80 days?
a)
1 Hour
b)
2 Hours
c)
3 Hours
d)
4 Hours
e)
None of these
 | Arya Roy answered |
Angel can do a piece of work in 10 days, Balu in 15 days. They work together for 5 days, the rest of the work is finished by Chitra in two more days. If they get Rs. 6000 as wages for the whole work, what are the daily wages of Angel, Bala and Chitra respectively?- a)200, 250, 300
- b)300, 200, 250
- c)600, 400, 200
- d)600, 400, 500
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Angel can do a piece of work in 10 days, Balu in 15 days. They work together for 5 days, the rest of the work is finished by Chitra in two more days. If they get Rs. 6000 as wages for the whole work, what are the daily wages of Angel, Bala and Chitra respectively?
a)
200, 250, 300
b)
300, 200, 250
c)
600, 400, 200
d)
600, 400, 500
e)
None of these
| | Bank Exams India answered |
Angel’s 5 days work = 50%
Balu’s 5 days work = 33.33%
Chitra’s 2 days work = 16.66%
[100- (50+33.33)]
Ratio of work of Angel, Balu and Chitra = 3: 2: 1
Angel’s total share = Rs. 3000
Balu’s total share = Rs. 2000
Chitra’s total share = Rs. 1000
Angel’s one day’s wage = Rs.600
Balu’s one day’s wage = Rs.400
Chitra’s one day’s wage = Rs.500
Balu’s 5 days work = 33.33%
Chitra’s 2 days work = 16.66%
[100- (50+33.33)]
Ratio of work of Angel, Balu and Chitra = 3: 2: 1
Angel’s total share = Rs. 3000
Balu’s total share = Rs. 2000
Chitra’s total share = Rs. 1000
Angel’s one day’s wage = Rs.600
Balu’s one day’s wage = Rs.400
Chitra’s one day’s wage = Rs.500
Ravi can do a piece of work in 16 days. Rakesh can do the same work in 64/5 days, while Geeta can do it in 32 days. All of them started to work together but Ravi leaves after 4 days. Rakesh leaves the job 3 days before the completion of the work. How long would the work last?- a)6 days
- b)9 days
- c)18 days
- d)5 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Ravi can do a piece of work in 16 days. Rakesh can do the same work in 64/5 days, while Geeta can do it in 32 days. All of them started to work together but Ravi leaves after 4 days. Rakesh leaves the job 3 days before the completion of the work. How long would the work last?
a)
6 days
b)
9 days
c)
18 days
d)
5 days
e)
None of these
| | Kavya Saxena answered |
Let the work lasted for x days,
Ravi’s 4 day’s work + Rakesh (x – 3) day’s work + Geeta’s x day’s work = 1
⇒ (4/16) + (x – 3) / (64/5) + x/32 = 1
⇒ 5(x – 3)/64 + x/32 = 1 – 1/4
⇒ [5(x – 3) + 2x] / 64 = 3/4
⇒ 7x – 15 = 48
∴ x = (48 + 15)/7 = 63/7 = 9 days
Ravi’s 4 day’s work + Rakesh (x – 3) day’s work + Geeta’s x day’s work = 1
⇒ (4/16) + (x – 3) / (64/5) + x/32 = 1
⇒ 5(x – 3)/64 + x/32 = 1 – 1/4
⇒ [5(x – 3) + 2x] / 64 = 3/4
⇒ 7x – 15 = 48
∴ x = (48 + 15)/7 = 63/7 = 9 days
Working together Bala and Chitra take 50% more number of days than Angel, Bala and Chitra together take and Angel and Bala working together, take 8/3 more number of days than Angel, Bala and Chitra take together. If Angel, Bala and Chitra all have worked together till the completion of the work and Bala has received Rs.120 out of total earnings of Rs. 480 then in how many days did Angel, Bala and Chitra together complete the whole work?- a)2 days
- b)4 days
- c)6 days
- d)8 days
- e)5 days
Correct answer is option 'E'. Can you explain this answer?
Working together Bala and Chitra take 50% more number of days than Angel, Bala and Chitra together take and Angel and Bala working together, take 8/3 more number of days than Angel, Bala and Chitra take together. If Angel, Bala and Chitra all have worked together till the completion of the work and Bala has received Rs.120 out of total earnings of Rs. 480 then in how many days did Angel, Bala and Chitra together complete the whole work?
a)
2 days
b)
4 days
c)
6 days
d)
8 days
e)
5 days
 | Future Foundation Institute answered |
The days ratio of (Angel + Bala + Chitra) : (Bala + Chitra) = X:3X/2 = 2X:3x;
Efficiency ratio = 3X:2X
Efficiency of Angel = x.
(480/3X) = Rs.160
Amount received by Bala = Rs.120 & Chitra = 200
160:120:200 =4:3:5
1/4:1/3:1/5= 15:20:12;
(1/15+1/12+1/20)*Y = 1
Y = 5 days
Efficiency ratio = 3X:2X
Efficiency of Angel = x.
(480/3X) = Rs.160
Amount received by Bala = Rs.120 & Chitra = 200
160:120:200 =4:3:5
1/4:1/3:1/5= 15:20:12;
(1/15+1/12+1/20)*Y = 1
Y = 5 days
A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by A to complete the work independently.- a)80/3 days
- b)100/3 days
- c)60/3 days
- d)140/3 days
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by A to complete the work independently.
a)
80/3 days
b)
100/3 days
c)
60/3 days
d)
140/3 days
e)
None of these
| | Faizan Khan answered |
Let B complete the work in X days so in one day work done by B is 1/x
as A do half work in one-sixth of the time so A will complete work in 2*x/6 = x/3 days
One day work of A and B i.e. 3/x + 1/x = 1/20. So we get x = 80
So time taken by A alone = 80/3 days
as A do half work in one-sixth of the time so A will complete work in 2*x/6 = x/3 days
One day work of A and B i.e. 3/x + 1/x = 1/20. So we get x = 80
So time taken by A alone = 80/3 days
Nakul and Ram are working on aproduction company. Nakul takes 6 hours to make 32 products, while Ram takes 5 hours to make 40 products. How much time will they take, working together to make 110 products?- a)8 hours
- b)8 hours 15 minutes
- c)9 hours
- d)8 hours 25 minutes
- e)9 hours 15 minutes
Correct answer is option 'B'. Can you explain this answer?
Nakul and Ram are working on aproduction company. Nakul takes 6 hours to make 32 products, while Ram takes 5 hours to make 40 products. How much time will they take, working together to make 110 products?
a)
8 hours
b)
8 hours 15 minutes
c)
9 hours
d)
8 hours 25 minutes
e)
9 hours 15 minutes
 | Pratibha Ekka answered |
B
Ram and shyam can do a piece of work in 5 and 7 days respectively. They start working alternatively starting from shyam, then in how many days the work is completed- a)5.(3/7) days
- b)6.(5/7) days
- c)7.(5/6) days
- d)5.(6/7) days
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Ram and shyam can do a piece of work in 5 and 7 days respectively. They start working alternatively starting from shyam, then in how many days the work is completed
a)
5.(3/7) days
b)
6.(5/7) days
c)
7.(5/6) days
d)
5.(6/7) days
e)
None of these
| | Alok Verma answered |
1/7 + 1/5 = 12/35 this much work is completed in 2 days.
So 24/35 will be completed in 4 days
In the next day, 29/35 work get completed in 5 days, so remaining work will be completed by Ram in 6/7 days
So 24/35 will be completed in 4 days
In the next day, 29/35 work get completed in 5 days, so remaining work will be completed by Ram in 6/7 days
(x-2) person can do a work in x days and (x+7) person can do 75% of the same work in (x-10)days. Then in how many days can (x+10) person finish the work?- a)27 days
- b)12 days
- c)25 days
- d)18 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
(x-2) person can do a work in x days and (x+7) person can do 75% of the same work in (x-10)days. Then in how many days can (x+10) person finish the work?
a)
27 days
b)
12 days
c)
25 days
d)
18 days
e)
None of these
| | Aarav Sharma answered |
Given:
(x-2) person can do a work in x days
(x+7) person can do 75% of the same work in (x-10) days
To find:
In how many days can (x+10) person finish the work?
Solution:
Let us assume that the work done is 1 unit.
So, (x-2) persons can do 1 unit of work in x days.
Hence, the work done by 1 person in 1 day = 1/(x(x-2))
(x+7) persons can do 75% of the same work in (x-10) days.
So, the work done by (x+7) persons in 1 day = 0.75/ (x-10)
Let the number of days required for (x+10) persons to complete the work be d.
So, the work done by (x+10) persons in 1 day = 1/d
Now, we know that the work done is the same in all the cases.
Hence, we can equate the work done by (x-2) persons to the work done by (x+7) persons and (x+10) persons.
(x-2)/x = 0.75/(x-10) = (x+10)/d
Solving for d, we get d = 12 days.
Hence, (x+10) persons can finish the work in 12 days.
Answer: Option B) 12 days
(x-2) person can do a work in x days
(x+7) person can do 75% of the same work in (x-10) days
To find:
In how many days can (x+10) person finish the work?
Solution:
Let us assume that the work done is 1 unit.
So, (x-2) persons can do 1 unit of work in x days.
Hence, the work done by 1 person in 1 day = 1/(x(x-2))
(x+7) persons can do 75% of the same work in (x-10) days.
So, the work done by (x+7) persons in 1 day = 0.75/ (x-10)
Let the number of days required for (x+10) persons to complete the work be d.
So, the work done by (x+10) persons in 1 day = 1/d
Now, we know that the work done is the same in all the cases.
Hence, we can equate the work done by (x-2) persons to the work done by (x+7) persons and (x+10) persons.
(x-2)/x = 0.75/(x-10) = (x+10)/d
Solving for d, we get d = 12 days.
Hence, (x+10) persons can finish the work in 12 days.
Answer: Option B) 12 days
Ramu, Hari and Sanjay are three typists, who working simultaneously, can type 228 pages in four hours. In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ramu. During a period of five hours, Sanjay can type as many passages as Ramu can, during seven hours. How many pages does each of them type per hour?- a)16, 18, 22
- b)14, 17, 20
- c)15, 17, 22
- d)15, 18, 21
- e)16, 19, 22
Correct answer is option 'E'. Can you explain this answer?
Ramu, Hari and Sanjay are three typists, who working simultaneously, can type 228 pages in four hours. In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ramu. During a period of five hours, Sanjay can type as many passages as Ramu can, during seven hours. How many pages does each of them type per hour?
a)
16, 18, 22
b)
14, 17, 20
c)
15, 17, 22
d)
15, 18, 21
e)
16, 19, 22
| | Future Foundation Institute answered |
Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h. Therefore, they together can type 4(x + y + z) pages in 4 h
∴ 4(x + y + z) = 228
⇒ x + y + z = 57 …..(i)
Also, z – y = y – x
i.e., 2y = x + z ……(ii)
5z = 7x ……(iii)
From Eqs. (i) and (ii), we get
3y = 57
⇒ y = 19
From Eq. (ii), x + z = 38
x = 16 and z = 22
∴ 4(x + y + z) = 228
⇒ x + y + z = 57 …..(i)
Also, z – y = y – x
i.e., 2y = x + z ……(ii)
5z = 7x ……(iii)
From Eqs. (i) and (ii), we get
3y = 57
⇒ y = 19
From Eq. (ii), x + z = 38
x = 16 and z = 22
Madhavan can finish a work in 5 hours. He invites Manohar and Manjima who can work 3/4th as fast as he can to join him. He also invites Mani and Mohan who can work only 1/5th as fast as he can to join him. If the five person team works the same job and they start together, how long will it take for them to finish the job?- a)50/97 days
- b)87 days
- c)50/29 days
- d)78 days
- e)62 days
Correct answer is option 'C'. Can you explain this answer?
Madhavan can finish a work in 5 hours. He invites Manohar and Manjima who can work 3/4th as fast as he can to join him. He also invites Mani and Mohan who can work only 1/5th as fast as he can to join him. If the five person team works the same job and they start together, how long will it take for them to finish the job?
a)
50/97 days
b)
87 days
c)
50/29 days
d)
78 days
e)
62 days
| | Anaya Patel answered |
Let the work be 100 units.
Madhavan’s 1 hour work = 100/5 = 20 units
Manohar and Manjima’s 1 day work = 3/4 × 20 = 15 units.
Mohan and Mani’s 1 day work = 1/5 × 20 = 4 units.
In one day all five of them can do = 20 + 15 + 15 + 4 + 4 = 58 units of work. Hence they can complete the work in 100/58 days.
Madhavan’s 1 hour work = 100/5 = 20 units
Manohar and Manjima’s 1 day work = 3/4 × 20 = 15 units.
Mohan and Mani’s 1 day work = 1/5 × 20 = 4 units.
In one day all five of them can do = 20 + 15 + 15 + 4 + 4 = 58 units of work. Hence they can complete the work in 100/58 days.
Sruthi, Swetha and Swati together can cut 216 Apples of the same size in 3 hours. Number of Apples cut by Sruthi in 9 hours is same as the number of Apples cut by Swati in 7 hours. In one hour, Swati can cut as many Apples more than Swetha as Swetha can cut more than Sruthi.Then the number of Apples cut by Swetha in one hour?- a)21
- b)24
- c)27
- d)29
- e)None
Correct answer is option 'B'. Can you explain this answer?
Sruthi, Swetha and Swati together can cut 216 Apples of the same size in 3 hours. Number of Apples cut by Sruthi in 9 hours is same as the number of Apples cut by Swati in 7 hours. In one hour, Swati can cut as many Apples more than Swetha as Swetha can cut more than Sruthi.Then the number of Apples cut by Swetha in one hour?
a)
21
b)
24
c)
27
d)
29
e)
None
| | Aruna Singh answered |
Let's denote:
- Sruthi's efficiency as 'S' apples/hour
- Swetha's efficiency as 'W' apples/hour
- Swati's efficiency as 'T' apples/hour
Given information:
- S * 9 = T * 7 => S = (7/9)T
- T - W = W - S => T = 2W - S
Total work done in 3 hours:
- (S + W + T) * 3 = 216
- S + W + T = 72
Substituting S and T in terms of W:
- (7/9)T + W + 2W - (7/9)T = 72
- 3W = 72
- W = 24
Therefore, Swetha can cut 24 apples in one hour.
So, the correct answer is option B: 24.
P can do a piece of work in 20 days. Q is 25 percent more efficient than P. In how many days half the work is completed when both are working simultaneously?- a)41/9
- b)40/9
- c)39/9
- d)43/9
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
P can do a piece of work in 20 days. Q is 25 percent more efficient than P. In how many days half the work is completed when both are working simultaneously?
a)
41/9
b)
40/9
c)
39/9
d)
43/9
e)
None of these
| | Aisha Gupta answered |
Q is 25 percent more efficient so he will complete the work in 16 days
(1/20 + 1/16)*t = 1/2
(1/20 + 1/16)*t = 1/2
A and B can do a piece of work in 20 and 25 days respectively. They began to work together but A leaves after some days and B completed the remaining work in 12 days. Number of days after which A left the job- a)52/9 days
- b)67/9 days
- c)77/9 days
- d)117/9 days
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
A and B can do a piece of work in 20 and 25 days respectively. They began to work together but A leaves after some days and B completed the remaining work in 12 days. Number of days after which A left the job
a)
52/9 days
b)
67/9 days
c)
77/9 days
d)
117/9 days
e)
None of these
 | Ravi Singh answered |
(1/20 + 1/25)*T + 12/25 = 1
We will get T = 52/9 days
We will get T = 52/9 days
A group of 24 women is supposed to do a work in 40 days. After 20 days 4 more women is employed and the work is completed in 2 days before the scheduled time. How many days it have been delayed if 4 more women were not employed?- a)1 day
- b)2 day
- c)3 day
- d)4 day
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
A group of 24 women is supposed to do a work in 40 days. After 20 days 4 more women is employed and the work is completed in 2 days before the scheduled time. How many days it have been delayed if 4 more women were not employed?
a)
1 day
b)
2 day
c)
3 day
d)
4 day
e)
None of these
| | Anaya Patel answered |
24*20 + 28*18 = total work = 24*T (T is the number of days when 4 more women are not employed)
we get T = 41, so work will be delayed by 1 day
we get T = 41, so work will be delayed by 1 day
When Ashok and Karthik are working alone, they can complete a piece of work in 25 days and 30 days respectively. On day 1, Karthik started the work and Ashok joined B from day 3 on-wards. Find approximately after how many days will the work be completed?- a)20 days
- b)10 days
- c)15 days
- d)25 days
- e)30 days
Correct answer is option 'C'. Can you explain this answer?
When Ashok and Karthik are working alone, they can complete a piece of work in 25 days and 30 days respectively. On day 1, Karthik started the work and Ashok joined B from day 3 on-wards. Find approximately after how many days will the work be completed?
a)
20 days
b)
10 days
c)
15 days
d)
25 days
e)
30 days
| | Aisha Gupta answered |
Fraction of work completed by Karthik on day 1 and day 2 = 2* 1/30 = 1/15
Fraction of work left after 2 days = 14/15
Fraction of work completed by Both = 1/25 + 1/30 = 11/150
Number of days after day 2 to complete work = 14*150/15*11 = 13 days
So after 2+13 = 15 days works will be completed
Fraction of work left after 2 days = 14/15
Fraction of work completed by Both = 1/25 + 1/30 = 11/150
Number of days after day 2 to complete work = 14*150/15*11 = 13 days
So after 2+13 = 15 days works will be completed
A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for six more days to finish the work. Find the number of days in which all the workers together will finish the work?- a)22 days
- b)20 days
- c)24 days
- d)35 days
- e)32 days
Correct answer is option 'D'. Can you explain this answer?
A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for six more days to finish the work. Find the number of days in which all the workers together will finish the work?
a)
22 days
b)
20 days
c)
24 days
d)
35 days
e)
32 days
 | Gowri Chakraborty answered |
Explanation :
30 workers work in pairs, with no same pair of workers working together twice
29[1/w1 + 1/w2 ….. + 1/w30] + 6[1/w1 + 1/w2 ….. + 1/w30] = 1
[1/w1 + 1/w2 ….. + 1/w30] = 1/35
35 days.
50 men could complete a work in 200 days. They worked together for 150 days, after that due to bad weather the work is stopped for 25 days. How many more workers should be employed so as to complete the work in time?- a)25
- b)35
- c)50
- d)60
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
50 men could complete a work in 200 days. They worked together for 150 days, after that due to bad weather the work is stopped for 25 days. How many more workers should be employed so as to complete the work in time?
a)
25
b)
35
c)
50
d)
60
e)
None of these
| | Ravi Singh answered |
Let additional workers be P, (50*150)/(50*200) = 3/4 of the work is already completed and now only 1/4 of the work is to be done. So,
1/4 = ((50 + P) * 25)/50*200, solve for p, we get P = 50
1/4 = ((50 + P) * 25)/50*200, solve for p, we get P = 50
Three professors P, Q, R are evaluating answer script of a subject. P is 40 more efficient than Q, who is 20 more efficient than R. P takes 10 days less than Q to complete the evaluation work. P starts the evaluation work and works for 10 days and then Q takes over. Q evaluates for next 15 days and then stops. In how many days, R can complete the remaining evaluation work?- a)6.2 days
- b)7.2 days
- c)8.2 days
- d)9.2 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Three professors P, Q, R are evaluating answer script of a subject. P is 40 more efficient than Q, who is 20 more efficient than R. P takes 10 days less than Q to complete the evaluation work. P starts the evaluation work and works for 10 days and then Q takes over. Q evaluates for next 15 days and then stops. In how many days, R can complete the remaining evaluation work?
a)
6.2 days
b)
7.2 days
c)
8.2 days
d)
9.2 days
e)
None of these
| | KS Coaching Center answered |
Let R takes x days to complete the work, then
1/P = (140/100)*1/Q and 1/Q = (120/100)*1/R
So P will take 25x/42 and Q will take 5x/6 days respectively
5x/6 – 25x/42 = 10, we get x = 42
10/25 + 15/35 + t/42 = 1
1/P = (140/100)*1/Q and 1/Q = (120/100)*1/R
So P will take 25x/42 and Q will take 5x/6 days respectively
5x/6 – 25x/42 = 10, we get x = 42
10/25 + 15/35 + t/42 = 1
P and Q can do a piece of work in 10 days and 20 days respectively. Both of them start the work but P leaves the work 5 days before its completion. Find the time in which work is completed- a)10
- b)15
- c)20
- d)25
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
P and Q can do a piece of work in 10 days and 20 days respectively. Both of them start the work but P leaves the work 5 days before its completion. Find the time in which work is completed
a)
10
b)
15
c)
20
d)
25
e)
None of these
| | Alok Verma answered |
(1/10 + 1/20)*(T-5) + 5/20 = 1 (T is the number of days in which the work is completed)
Kiran can do a work in 20 days, while Karan can do the same work in 25 days. They started the work jointly. Few days later Suman also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.1000. What is the share of Suman?- a)200
- b)400
- c)100
- d)300
- e)500
Correct answer is option 'C'. Can you explain this answer?
Kiran can do a work in 20 days, while Karan can do the same work in 25 days. They started the work jointly. Few days later Suman also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.1000. What is the share of Suman?
a)
200
b)
400
c)
100
d)
300
e)
500
| | Aarav Sharma answered |
Efficiency of Kiran = 5%
Efficiency of Karan = 4%
They will complete only 90% of the work = [(5+4)*10] = 90
Remaining work done by Suman = 10%.
Share of Suman = 10/100 * 1000 = 100
Efficiency of Karan = 4%
They will complete only 90% of the work = [(5+4)*10] = 90
Remaining work done by Suman = 10%.
Share of Suman = 10/100 * 1000 = 100
When pipes A and C were open, the tank was filled in 50 minutes. If Pipe A can fill the tank in 30 minutes, in how many minutes can Pipe C empty the filled tank?- a)60
- b)75
- c)90
- d)120
Correct answer is option 'B'. Can you explain this answer?
When pipes A and C were open, the tank was filled in 50 minutes. If Pipe A can fill the tank in 30 minutes, in how many minutes can Pipe C empty the filled tank?
a)
60
b)
75
c)
90
d)
120
 | Bayshore Academy answered |
Therefore, Pipe C can empty the filled tank in 75 minutes.
A can do a piece of work in 20 days and B can do the same work in 30 days. In how many days can both finish the whole work working together?- a)10
- b)12
- c)15
- d)18
Correct answer is option 'B'. Can you explain this answer?
A can do a piece of work in 20 days and B can do the same work in 30 days. In how many days can both finish the whole work working together?
a)
10
b)
12
c)
15
d)
18
 | Pranab Goyal answered |
Working together to finish a piece of work:
To determine how many days it will take for A and B to finish the work together, we need to calculate their combined work rate.
Work rate of A and B:
- A can finish the work in 20 days, so A's work rate = 1/20.
- B can finish the work in 30 days, so B's work rate = 1/30.
Combined work rate:
When A and B work together, their combined work rate is the sum of their individual work rates. Therefore, their combined work rate = 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12.
Calculating the number of days to finish the work together:
To find out how many days it will take for A and B to finish the work together, we use the formula:
Number of days = Total work / Combined work rate
Since the total work is 1, and the combined work rate is 1/12, we have:
Number of days = 1 / (1/12) = 12 days.
Therefore, A and B will finish the whole work working together in 12 days, which corresponds to option B.
To determine how many days it will take for A and B to finish the work together, we need to calculate their combined work rate.
Work rate of A and B:
- A can finish the work in 20 days, so A's work rate = 1/20.
- B can finish the work in 30 days, so B's work rate = 1/30.
Combined work rate:
When A and B work together, their combined work rate is the sum of their individual work rates. Therefore, their combined work rate = 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12.
Calculating the number of days to finish the work together:
To find out how many days it will take for A and B to finish the work together, we use the formula:
Number of days = Total work / Combined work rate
Since the total work is 1, and the combined work rate is 1/12, we have:
Number of days = 1 / (1/12) = 12 days.
Therefore, A and B will finish the whole work working together in 12 days, which corresponds to option B.
Sarthak can destroy a work in 90 days and Deepak can destroy the same work in 60 days. In how many days can both of them together destroy the work?- a)30
- b)36
- c)40
- d)42
Correct answer is option 'B'. Can you explain this answer?
Sarthak can destroy a work in 90 days and Deepak can destroy the same work in 60 days. In how many days can both of them together destroy the work?
a)
30
b)
36
c)
40
d)
42
 | Malavika Rane answered |
Understanding Individual Work Rates
Sarthak and Deepak have different work rates based on how many days they take to complete the same task.
- Sarthak's Work Rate:
- He can complete the work in 90 days.
- Work rate = 1/90 (work done per day)
- Deepak's Work Rate:
- He can complete the work in 60 days.
- Work rate = 1/60 (work done per day)
Combined Work Rate Calculation
To find out how quickly they can complete the work together, we add their individual work rates.
- Combined Work Rate:
- Combined work rate = Sarthak's rate + Deepak's rate
- Combined work rate = 1/90 + 1/60
Finding a Common Denominator
To add these fractions, we find a common denominator.
- Common Denominator of 90 and 60:
- The least common multiple (LCM) of 90 and 60 is 180.
- Converting Fractions:
- Sarthak's rate: (1/90) = 2/180
- Deepak's rate: (1/60) = 3/180
Final Calculation
Now we can add the two rates:
- Combined Rate:
- Combined work rate = 2/180 + 3/180 = 5/180
- Simplifying gives us 1/36.
Time to Complete Work Together
To find out how long it takes both of them to complete the work, we take the reciprocal of their combined work rate.
- Time Taken Together:
- Time = 1 / (1/36) = 36 days.
Thus, Sarthak and Deepak together can destroy the work in 36 days. Therefore, the correct answer is option 'B'.
Sarthak and Deepak have different work rates based on how many days they take to complete the same task.
- Sarthak's Work Rate:
- He can complete the work in 90 days.
- Work rate = 1/90 (work done per day)
- Deepak's Work Rate:
- He can complete the work in 60 days.
- Work rate = 1/60 (work done per day)
Combined Work Rate Calculation
To find out how quickly they can complete the work together, we add their individual work rates.
- Combined Work Rate:
- Combined work rate = Sarthak's rate + Deepak's rate
- Combined work rate = 1/90 + 1/60
Finding a Common Denominator
To add these fractions, we find a common denominator.
- Common Denominator of 90 and 60:
- The least common multiple (LCM) of 90 and 60 is 180.
- Converting Fractions:
- Sarthak's rate: (1/90) = 2/180
- Deepak's rate: (1/60) = 3/180
Final Calculation
Now we can add the two rates:
- Combined Rate:
- Combined work rate = 2/180 + 3/180 = 5/180
- Simplifying gives us 1/36.
Time to Complete Work Together
To find out how long it takes both of them to complete the work, we take the reciprocal of their combined work rate.
- Time Taken Together:
- Time = 1 / (1/36) = 36 days.
Thus, Sarthak and Deepak together can destroy the work in 36 days. Therefore, the correct answer is option 'B'.
Diya can complete a work in 80 days. In how many days can she complete it with 80% of her efficiency?- a)60
- b)70
- c)80
- d)100
Correct answer is option 'D'. Can you explain this answer?
Diya can complete a work in 80 days. In how many days can she complete it with 80% of her efficiency?
a)
60
b)
70
c)
80
d)
100
 | Ishaan Roy answered |
Understanding Diya's Work Efficiency
Diya can complete a task in 80 days at her full efficiency. To determine how long it will take her to complete the same task at 80% of her efficiency, we need to understand the impact of efficiency on time taken.
Calculating Diya's Work Rate
- At full efficiency, Diya completes 1/80 of the work in a day.
- This means she completes 1 unit of work in 80 days.
Adjusting for 80% Efficiency
- 80% of her efficiency means she is now completing only 80% of her usual daily work.
- Thus, her new work rate will be:
- (1/80) * 80% = 1/100 per day.
Finding the New Time Required
- If Diya completes 1/100 of the work in a day, we can determine how many days it will take her to complete the entire work:
- Total work = 1 unit.
- Days required = Total work / New daily work rate = 1 / (1/100) = 100 days.
Conclusion
- Therefore, at 80% efficiency, Diya will take 100 days to complete the work.
The correct answer is option D: 100 days.
Diya can complete a task in 80 days at her full efficiency. To determine how long it will take her to complete the same task at 80% of her efficiency, we need to understand the impact of efficiency on time taken.
Calculating Diya's Work Rate
- At full efficiency, Diya completes 1/80 of the work in a day.
- This means she completes 1 unit of work in 80 days.
Adjusting for 80% Efficiency
- 80% of her efficiency means she is now completing only 80% of her usual daily work.
- Thus, her new work rate will be:
- (1/80) * 80% = 1/100 per day.
Finding the New Time Required
- If Diya completes 1/100 of the work in a day, we can determine how many days it will take her to complete the entire work:
- Total work = 1 unit.
- Days required = Total work / New daily work rate = 1 / (1/100) = 100 days.
Conclusion
- Therefore, at 80% efficiency, Diya will take 100 days to complete the work.
The correct answer is option D: 100 days.
A, B and C together can complete a work in 8 days. If A is 50% more efficient than B and B is 50% less efficient than C, then B alone will complete the same work in:- a)16 days
- b)24 days
- c)48 days
- d)36 days
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
A, B and C together can complete a work in 8 days. If A is 50% more efficient than B and B is 50% less efficient than C, then B alone will complete the same work in:
a)
16 days
b)
24 days
c)
48 days
d)
36 days
e)
None of these
 | Mihir Chawla answered |
Solution:
Let's assume that C can complete the work in x days.
Efficiency of B compared to C:
B is 50% less efficient than C. This means B can complete only half the work that C can complete in the same time. So, B can complete the work in 2x days.
Efficiency of A compared to B:
A is 50% more efficient than B. This means A can complete 1.5 times the work that B can complete in the same time. So, A can complete the work in (2x/1.5) days.
Efficiency of A, B, and C together:
Given that A, B, and C together can complete the work in 8 days. So, their combined efficiency is 1/8 of the work per day.
Let's calculate their combined efficiency:
1/A + 1/B + 1/C = 1/8
Substituting the values of A, B, and C:
1/(2x/1.5) + 1/2x + 1/x = 1/8
Taking the LCM and simplifying the equation:
[(1.5 + 3 + 4)/2x] = 1/8
8/2x = 1/8
2x = 64
x = 32
So, C alone can complete the work in 32 days.
Now, let's find out how many days B alone will take to complete the work:
B can complete the work in 2x days.
Substituting the value of x:
B can complete the work in 2(32) = 64 days.
Therefore, the correct answer is option D) 36 days.
Let's assume that C can complete the work in x days.
Efficiency of B compared to C:
B is 50% less efficient than C. This means B can complete only half the work that C can complete in the same time. So, B can complete the work in 2x days.
Efficiency of A compared to B:
A is 50% more efficient than B. This means A can complete 1.5 times the work that B can complete in the same time. So, A can complete the work in (2x/1.5) days.
Efficiency of A, B, and C together:
Given that A, B, and C together can complete the work in 8 days. So, their combined efficiency is 1/8 of the work per day.
Let's calculate their combined efficiency:
1/A + 1/B + 1/C = 1/8
Substituting the values of A, B, and C:
1/(2x/1.5) + 1/2x + 1/x = 1/8
Taking the LCM and simplifying the equation:
[(1.5 + 3 + 4)/2x] = 1/8
8/2x = 1/8
2x = 64
x = 32
So, C alone can complete the work in 32 days.
Now, let's find out how many days B alone will take to complete the work:
B can complete the work in 2x days.
Substituting the value of x:
B can complete the work in 2(32) = 64 days.
Therefore, the correct answer is option D) 36 days.
Manoj can complete 75% of a work in 90 days. In how many days can he complete 80% of that work with his full efficiency?- a)60
- b)72
- c)80
- d)96
Correct answer is option 'D'. Can you explain this answer?
Manoj can complete 75% of a work in 90 days. In how many days can he complete 80% of that work with his full efficiency?
a)
60
b)
72
c)
80
d)
96
| | Pranab Goyal answered |
Understanding the Problem
Manoj can complete 75% of a work in 90 days. We need to calculate how many days he would take to complete 80% of the same work.
Calculating Work Rate
- If 75% of the work takes 90 days, we can find the total amount of work in days.
- The full work (100%) would take:
- (90 days / 75%) = 90 days * (100/75) = 120 days.
Daily Work Output
- Manoj’s work rate can be computed as follows:
- Total work = 1 (100% of the work).
- Daily work output = 1 work / 120 days = 1/120 work per day.
Calculating Time for 80% of Work
- To find the time taken to complete 80% of the work:
- Work to be done = 80% of the total work = 0.8.
- Time required = Work to be done / Daily work output = 0.8 / (1/120) = 0.8 * 120 = 96 days.
Final Answer
- Therefore, Manoj can complete 80% of the work in 96 days.
The correct option is D) 96.
Manoj can complete 75% of a work in 90 days. We need to calculate how many days he would take to complete 80% of the same work.
Calculating Work Rate
- If 75% of the work takes 90 days, we can find the total amount of work in days.
- The full work (100%) would take:
- (90 days / 75%) = 90 days * (100/75) = 120 days.
Daily Work Output
- Manoj’s work rate can be computed as follows:
- Total work = 1 (100% of the work).
- Daily work output = 1 work / 120 days = 1/120 work per day.
Calculating Time for 80% of Work
- To find the time taken to complete 80% of the work:
- Work to be done = 80% of the total work = 0.8.
- Time required = Work to be done / Daily work output = 0.8 / (1/120) = 0.8 * 120 = 96 days.
Final Answer
- Therefore, Manoj can complete 80% of the work in 96 days.
The correct option is D) 96.
Sanjay can do a piece of work in 50 days. He started the work and left after some days, when 25% work was done. After it Ajit joined and completed it working for 25 days. In how many days Sanjay and Ajit can do the complete work, working together?- a)6
- b)8
- c)10
- d)12
- e)20
Correct answer is option 'E'. Can you explain this answer?
Sanjay can do a piece of work in 50 days. He started the work and left after some days, when 25% work was done. After it Ajit joined and completed it working for 25 days. In how many days Sanjay and Ajit can do the complete work, working together?
a)
6
b)
8
c)
10
d)
12
e)
20
 | Nikita Singh answered |
Efficiency of Sanjay = (100/50) = 2%
Rest work = 75%
∴ Efficiency of Ajit = 75/25 = 3%
∴ Combined efficiency of Sanjay and Ajit = 5%
∴ Number of days required by Sonu and Abhijeet, to work together = 100/5 = 20 days.
Rest work = 75%
∴ Efficiency of Ajit = 75/25 = 3%
∴ Combined efficiency of Sanjay and Ajit = 5%
∴ Number of days required by Sonu and Abhijeet, to work together = 100/5 = 20 days.
P can do a piece of work in 20 days. Q is 25 percent more efficient than P. In how many days half the work is completed when both are working simultaneously?- a)41/9
- b)40/9
- c)39/9
- d)43/9
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
P can do a piece of work in 20 days. Q is 25 percent more efficient than P. In how many days half the work is completed when both are working simultaneously?
a)
41/9
b)
40/9
c)
39/9
d)
43/9
e)
None of these
| | Rajeev Kumar answered |
Q is 25 percent more efficient so he will complete the work in 16 days
(1/20 + 1/16)*t = 1/2
(1/20 + 1/16)*t = 1/2
A and B undertake to complete a piece of work for Rupees 1200. A can do it in 8 days, B can do it in 12 days and with the help of C they complete the work in 4 days. Find the share of C?- a)100
- b)200
- c)300
- d)400
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
A and B undertake to complete a piece of work for Rupees 1200. A can do it in 8 days, B can do it in 12 days and with the help of C they complete the work in 4 days. Find the share of C?
a)
100
b)
200
c)
300
d)
400
e)
None of these
| | Alok Verma answered |
1/8 + 1/12 + 1/C = 1/4, we get C = 24 days
now efficiency of A, B and C are in the ratio of 1/8 :1/12 : 1/24
3:2:1, so share of C is 1/6 * 1200 = 200
now efficiency of A, B and C are in the ratio of 1/8 :1/12 : 1/24
3:2:1, so share of C is 1/6 * 1200 = 200
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