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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?

Solution:

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

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?

Solution:

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

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.

Solution:

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

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

Solution:

(1/20 + 1/25)*T + 12/25 = 1

We will get T = 52/9 i.e. 5.7/9 days

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.

Solution:

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

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?

Solution:

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

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?

Solution:

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

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?

Solution:

Q is 25 percent more efficient so he will complete the work in 16 days

(1/20 + 1/16)*t = 1/2

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?

Solution:

1/A + 1/B = 1/24 , 1/B + 1/C = 1/32

10/A + 14/B + 26/C = 1

10(1/A + 1/B) + 4(1/B + 1/C) + 22/C = 1

10/24 + 4/32 + 22/C = 1, we get C = 48 days

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?

Solution:

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

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

Solution:

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

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

Solution:

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

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

Solution:

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

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?

Solution:

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

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?

Solution:

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

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?

Solution:

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

QUESTION: 17

Solution:

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

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?

Solution:

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

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.

Solution:

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

QUESTION: 20

Solution:

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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