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Numerical Aptitude (Chapter : Time and Work)

Work

Work to be done is generally considered as one unit. It may be digging a trench constructing or painting a wall, filling up or emptying a tank, reservoir or a cistern.

General rules to be followed in the problems on Time and Work

1. If A can do a piece of work in n days, then work done by A in 1 day is I/n. i.e, if a person can do some work in 12 days, he does 1/ 12th of the work in one day.
2. If A’s 1 day’s work = 1/n, then A can finish the whole work in n days. ie, if a person’s one day work is 1/10, then he can finish the whole work in 10 days.
3. If A is thrice as good a workman as B, then ratio of work done by A and B = 3 : 1. ie, if a man works three times as fast as a woman does, then when the work is complete, 3 parts of the work has been done by the man and 1 part by the woman.
4. If A is thrice as good a workman as B, then ratio of time taken by A and B = 1 : 3. ie, if the woman takes 15 days to complete the work, then the man takes 5 days to complete the same work.
5. If two persons A and B can individually do some work in a and b days respectively, then A and B together can complete the same work in ab (a + b) days.
6. The fundamental rules on variation also apply in Time and Work.

1. Work and men are directly proportional to each other ie, if the work increases, the no. of men required to do it, also increases, if the work is to be completed in the same number of days.
2. Men and days are inversely proportional, i.e, if the number of men increases, the number of days required to complete the same work decreases and vice versa.
3. Work and days are directly proportional, i.e, if the work increases, the number of days required also increases, if the work is to be completed with the same number of men and vice versa.

Example 1: Ravi and Rishi can do a piece of work in 24 days, Rishi and Ronit in 30 days, Ronit and Ravi in 40 days. In how many days will they finish it together and separately?

Solution. (Ravi and Rishi)’s 1 day’s work =1/24

(Rishi and Ronit)’s 1 day’s work = 1/30

(Ronit and Ravi)’s 1 day’s work = 1/40

On adding, we get

2 (Ravi + Rishi + Ronit)’s 1 day’s work = (1/24 + 1/30 + 1/40) = 1/10

So, (Ravi + Rishi + Ronit)’s 1 day’s work = 1/20

So, they all together can finish the work in 20 days.

Ravi’s 1 day’s work = [(Ravi + Rishi + Ronit)’s 1 day’s work] – [(Rishi + Ronit)’s 1 day’s work]

= (1/20 – 1/30) = 1/60

So, Ravi alone can finish the work in 60 days.

Similarly, Rishi’s 1 day work = (1/20 – 1/40) = 1/40

So, Rishi alone can finish the work in 40 days

And Ronit’s 1 day work = (1/20 – 1/24)

= 1/120

So, Rishi alone can finish the work in 120 days.

Pipes and Cisterns

A pipe or a tap connected with a tank (or a cistern or a reservoir) is called an inlet, if it fills it. A pipe or a tap connected with a tank (or a cistern or a reservoir) is called an outlet, if it empties it.

:: Home Assignment for Practice ::

1.A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work?

(a) 16
(b) 24
(c) 37
(d) 48

2. A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was:

(a) 11
(b) 7
(c) 9
(d) 12

3. A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days to complete the work is:

(a) 33/5
(b)17/2
(c)51/5
(d)27/2

4. A, B and C can complete a work separately in 24, 36 and 48 days respectively. They started together but C left after 4 days of start and A left 3 days before the completion of the work. In how many days will the work be completed?

(a) 15 days
(b) 24 days
(c) 25 days
(d) 38 days

5. A, B and C together earn Rs300 per day, while A and C together earn Rs188 and B and C together earn Rs152. The daily earning of C is:

(a) Rs40
(b) Rs70
(c) Rs112
(d) Rs160

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