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Time And Work - MCQ 3


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20 Questions MCQ Test Quantitative Techniques for CLAT | Time And Work - MCQ 3

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Time And Work - MCQ 3 - Question 1

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?

Detailed Solution for Time And Work - MCQ 3 - Question 1

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

Time And Work - MCQ 3 - Question 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?

Detailed Solution for Time And Work - MCQ 3 - Question 2

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

Time And Work - MCQ 3 - Question 3

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.

Detailed Solution for Time And Work - MCQ 3 - Question 3

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

Time And Work - MCQ 3 - Question 4

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

Detailed Solution for Time And Work - MCQ 3 - Question 4

(1/20 + 1/25)*T + 12/25 = 1
We will get T = 52/9 i.e. 5.7/9 days

Time And Work - MCQ 3 - Question 5

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.

Detailed Solution for Time And Work - MCQ 3 - Question 5

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

Time And Work - MCQ 3 - Question 6

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?

Detailed Solution for Time And Work - MCQ 3 - Question 6

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

Time And Work - MCQ 3 - Question 7

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?

Detailed Solution for Time And Work - MCQ 3 - Question 7

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

Time And Work - MCQ 3 - Question 8

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?

Detailed Solution for Time And Work - MCQ 3 - Question 8

Q is 25 percent more efficient so he will complete the work in 16 days
(1/20 + 1/16)*t = 1/2

Time And Work - MCQ 3 - Question 9

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?

Detailed Solution for Time And Work - MCQ 3 - Question 9

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.

Time And Work - MCQ 3 - Question 10

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?

Detailed Solution for Time And Work - MCQ 3 - Question 10

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

Time And Work - MCQ 3 - Question 11

A and B can do a piece of work in 24 and 30 days respectively. Both started the work and worked for 6 days. Then B leaves the work and C joins and the remaining work is completed by A and C together in 11 days. Find the days in which C alone can do the work

Detailed Solution for Time And Work - MCQ 3 - Question 11

(1/24 + 1/30)*6 + (1/24 + 1/c)*11 = 1

Time And Work - MCQ 3 - Question 12

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

Detailed Solution for Time And Work - MCQ 3 - Question 12

(1/10 + 1/20)*(T-5) + 5/20 = 1 (T is the number of days in which the work is completed)

Time And Work - MCQ 3 - Question 13

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

Detailed Solution for Time And Work - MCQ 3 - Question 13

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

Time And Work - MCQ 3 - Question 14

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?

Detailed Solution for Time And Work - MCQ 3 - Question 14

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

Time And Work - MCQ 3 - Question 15

P, Q and R can do a piece of work in 16, 24 and 30 days respectively. They started the work simultaneously but P stops the work after 4 days and Q called off the work 2 days before the completion. In what time the work is finished?

Detailed Solution for Time And Work - MCQ 3 - Question 15

4/16 + (T -2)/24 + T/30 = 1 where T is the time taken to complete the job

Time And Work - MCQ 3 - Question 16

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?

Detailed Solution for Time And Work - MCQ 3 - Question 16

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

Time And Work - MCQ 3 - Question 17

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?

Detailed Solution for Time And Work - MCQ 3 - Question 17

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

Time And Work - MCQ 3 - Question 18

A does half as much work as B in one third of the time taken by B. If together they take 20 days to finish the work then what will be the share of A if 1000 rupees is given for the whole work?

Detailed Solution for Time And Work - MCQ 3 - Question 18

Let B take x days to complete the work, then A will take = x/3 + x/3 = 2x/3 days (as half work is completed in one third of the time) 3/2x + 1/x = 1/20
X = 50. So A will complete the work in 100/3 days and B will complete the work in 50 days.
Ratio of work done by A and B – 3/100: 1/50 = 3:2
So A share = 3/5*1000 = 600

Time And Work - MCQ 3 - Question 19

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.

Detailed Solution for Time And Work - MCQ 3 - Question 19

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

Time And Work - MCQ 3 - Question 20

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?

Detailed Solution for Time And Work - MCQ 3 - Question 20

Q is 25 percent more efficient so he will complete the work in 16 days
(1/20 + 1/16)*t = 1/2

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