 # Problems on Time and Work : Quantitative Aptitude

So, you are well prepared for the exam and have decided how much time you allot to every question for the best outcome of the exam. I am not going to discuss that point but the “Time And Work” problems asked in the eams.

Work is any action performed which takes some input and produces some output accordingly.

### Basic formulae and tricks

• More men can do more work
• More men can do same work in less time
• More work means more time required.
• More efficient men can do work quickly.

•    If  men can finish a work in days then

total work done = x*t

1. If A can do a piece of work in n days, work done by A in 1 day = 1/n

2. If A does 1/n work in a day, A can finish the work in n days

3. If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then

(M1 D1 H1) / W1 = (M2 D2 H2) / W2

4. If A can do a piece of work in p days and B can do the same in q days,

A and B together can finish it in pq / (p+q) days

5.  If A is thrice as good as B in work, then

The ratio of work done by A and B = 3: 1

The ratio of time taken to finish a work by A and B = 1 : 3

Here are some questions for your practice

Q1. P, Q, and R can completely solve a problem together in 4 hrs. P and R together take 15 hrs less than Q working alone. Q works on the problem for first 2 hrs and then P and R joins him. After another two hours, Q quits. In how many hours is the problem actually solved?

Sol.  Let Q alone can answer the problem in x hours
Then P&R together needs (x-15) hours to solve the problem

In 1 hr, Q can complete 1/x of the question,
In 1 hr, P&R can complete 1/(x-15) of the question
In 1 hr, P, Q, and R can complete 1/4th of the question

1/x + 1/(x-15) = 1/4
4(x-15)+4x =x(x-15)
4x – 60 + 4x = x^2 – 15x
x^2 – 23x + 60 = 0
(x-20)(x-3)=0
x = 20 or 3
since (x-15) is positive, x = 20

In 1 hr, Q can complete 1/20 of the question.
In 1 hr, P and R can complete 1/5 of the question
In 1 hr, P, Q, and R can complete 1/4 of the question

In the first two hours, 2* 1/20 = 1/10 of the question is completed by Q
P, Q, and R work in  next 2 hrs and completes 2 * 1/4 = 1/2 of the question

Remaining part  = 1 – 1/10 – 1/2 = 2/5
Let P&R work for n hours and completes this part
n = (2/5)/(1/5) = 2

Total time taken to solve the question = 2+2+2 = 6 hours

Q.2 A is twice as good a workman as B and is, therefore, able to finish a piece of work in 30 days less than B.In how many days they can complete the whole work; working together?

Sol.

The ratio of times taken by A and B = 1: 2.

The time difference is (2 – 1) 1 day while B takes 2 days and A takes 1 day.

If the difference of time is 1 day, B takes 2 days.

If the difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

A’s 1 day’s work = 1/30

B’s 1 day’s work = 1/60

(A + B)’s 1 day’s work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.

Q.3 A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 20 days and C alone in 60 days, then B alone could do it in

Sol.

(A+B)’s 1 day’s work=1/20

C’s 1 day work=1/60

(A+B+C)’s 1 day’s work= 1/20 + 1/60 = 1/15

Also A’s 1 day’s work =(B+C)’s 1 day’s work

Therefore,  we get: 2 x (A’s 1 day ‘s work)=1/15

=>A’s 1 day’s work=1/30

Therefore, B’s 1 day’s work= 1/20 – 1/30 = 1/60

So, B alone could do the work in 60 days

Q4. 12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working  and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day?

Sol.    1 man’s 1 day work =1/96 ; 1 woman’s 1 day work = 1/192

Work done in 6 days=6(896+8192)=6×18 =346896+8192=6×18 =34

Remaining work = 1/4

(8 men +8 women)’s 1 day work = 1(896+8192)1896+8192 =1/8

Remaining work =1/4 –  1/8 = 1/8

1/96 work is done in 1 day by 1 man

Therefore, 1/8 work will be done in 1 day by 96 x (1/8) =12 men

I think now you have got basic ideas about the questions , below I am providing you with some questions for practice.

Q1.  A is thrice efficient as B and C is twice as efficient as B. what is the ratio of the number of days taken by A, B, and C, when they work individually?
Q2.  The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:
Q3. A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?
Q4.Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?