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QUESTION: 1

A is twice efficient as B. A and B together do the same work in as much time as C and D can do together. If the ratio of the number of alone working days of C to D is 2:3 and if B worked 16 days more than C then no of days which A worked alone?

Solution:

Assume working days

A = x, B = 2x, C = 2y, D = 3y

1/x+1/2x = 1/2y+1/3y

And 2x-2y = 16

Solving we get x = 18 days

QUESTION: 2

A can do a piece of work in 40 days B can do the same piece of work in 60 days. A and B started the work together in the first 15 days A worked with 50% of his efficiency, in the next 15days B worked with 50% of his efficiency. Now in how many days does the remaining work will be completed if both of them work with their full efficiencies?

Solution:

15*(1/80+1/60) + 15*(1/120+1/40) + x*(1/40+1/60) = 1 X= 3/2 = 1.5

QUESTION: 3

A can do a piece of work in 30 days, B can do in 45 days and C can do same work alone in 60 days. If on the first day A worked alone and on the second day A and B worked together and on the third day A and C worked together. If they repeat the cycle as follows then in how many days total work can be completed?

Solution:

First day = 1/30

Second day = 1/30+1/45

Third day = 1/30+1/60

3 days work = 3/30+1/45+1/60 = 25/180

3*7 = 21 days work = 175/180

Now 1/36 work is left which can be completed by A alone

1/36*30 = 5/6

21+5/6 = 21 5/6 Days

QUESTION: 4

Ramu completes 30% of work in 7.5 days. Raju is 50% as efficient as Ramu, Venu is 50% as efficient as Raju. Now Raju and Venu joined with Ramu for the rest of the work then in how many days will take to complete the work?

Solution:

Ramu takes 25 days to complete work.

Raju = 50 days Venu = 100 days

Now 70% work is left

They can complete whole work in = 1/ 1/25+1/50+1/100

100/7 days then 70% in 10 days

QUESTION: 5

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?

Solution:

A = 21 B = 14 C =7

x/21+2*(1/14+1/7) = 1

x = 12.

QUESTION: 6

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?

Solution:

20*(5+6+7+8+4x)/840 = 1 x= 4 hours

QUESTION: 7

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?

Solution:

U+v+W = 72 9U = 7W W-V = V-U V = 24

QUESTION: 8

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?

Solution:

(1/5+1/4)

20/9*90/100 = 2

QUESTION: 9

If A and B work together can complete a work in 8/5 days. A started the work alone and completed. 50% of the work and left the work then B started the work alone and finished the rest of work. They took total 5 days to complete the work. Then in how many days B can complete the work if A is more efficient than A?

Solution:

1/A+1/B = 5/8

x/A+y/B = 1

x+y = 5

y = 4

QUESTION: 10

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?

Solution:

11*50/1/3 = (11+x)*50/2/3

X = 11

QUESTION: 11

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?

Solution:

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.

QUESTION: 12

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?

Solution:

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

QUESTION: 13

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:

Solution:

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.

QUESTION: 14

Chitra is twice efficient as Arun. Bala takes thrice as many days as Chitra. Arun takes 12 days to finish the work alone. If they work in pairs(i.e Arun-Bala, BalaChitra, Chitra-Arun) starting with Arun – Bala on the first day, Bala – Chitra on the second day and Chitra – Arun on the third day and so on, then how many days are required to finish the work?

Solution:

No of days taken by Arun = 12 days

No of days(Arun:Bala:Chitra) = 2:3:1

1 day work of (Arun+Bala) = 5/36

1 day work of (Bala+Chitra) = 8/36

1 day work of (Chitra+Arun) = 9/36

5 days total work – 35/36

1/36 is done by Arun-Chitra

Number of days taken by Arun-Chitra for the rest of the work = (1/36)/(9/36) = 1/9

Total time taken to complete the work = 5 + 1/9 = 46/9 days

QUESTION: 15

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?

Solution:

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.

QUESTION: 16

Arun can do a piece of work in 10 days, Bala 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. 5000 as wages for the whole work, what are the daily wages of Arun, Bala and Chitra respectively (in Rs)?

Solution:

A’s 5 days work = 50%

B’s 5 days work = 33.33%

C’s 2 days work = 16.66%[100- (50+33.33)] Ratio of contribution of work of Arun,

Bala and Chitra = 3 : 2 : 1

Arun’s total share = Rs. 3000

Bala’s total share = Rs. 2000

Chitra’s total share = Rs. 1000

Arun’s one day’s earning = Rs.600

Bala’s one day’s earning = Rs.400

Chitra’s one day’s earning = Rs.500

QUESTION: 17

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?

Solution:

D * x +(100- D) * 2x= 150x

⇒ D = 50 days

work done in 50 days = 50x

Total work = 150x

50x/150x * 100 = 100/3

QUESTION: 18

(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?

Solution:

3/4 * (x-2)x = (x+7)(x-10)

x – 6x – 280 = 0

x = 20; x = -14

(x-2)x = 18 * 20 = 360

360 = 30 * y

y = 12 days

QUESTION: 19

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?

Solution:

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

QUESTION: 20

Arun is twice efficient as Bala and together they do the same work in as much time as Chitra and David together. If Chitra and David can complete the work in 20 and 30 days respectively, working alone, then in how many days A can complete the work individually?

Solution:

1/x + 1/2x = 1/20 + 1/30

3/2x = 1/12

Number of days taken by Arun = 18 days

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