## TIME AND WORK

### Introduction

If A can do a work in ‘n’ days then he does 1/n work daily. If A is thrice as good as B at something then the ratio of their work done is 1:3.

• If A does a work in a days, then in one day A does 1a of the work. If B does a work in b days, then in one day B does 1b of the work. Then, in one day, if A and B work together, then their combined work is 1a+1b=a+bab

• For example, if A can do a work in 10 days and B can do the same work in 12 days, then the work will be completed in how many days. One day’s work = 1/10 + 1/12 = (12 + 10)/120. Then the number of days required to complete the work is 120/22.

• Instead of taking the value of the total work as 1 unit of work, we can also look at the total work as 100 per cent work. In such a case, the following rule applies: If A does a work in ‘a’ days, then in one day A does 100a% of the work. If B does a work in ‘b’ days, then in one day B does 100b% of the work. Then, in one day, if A and B work together, then their combined work is 100a+100b.

Q. If A can do a work in 10 days and B can do the same work in 12 days, then the work will be completed in how many days

• If A can do a work in 10 days (so means 10% work) and B can do the same work in 12 days (so 8.33% work so 18.33% work in a day in 5 days 91.66% work so leaves 8.33% work to be done so which can be done in 8.33/18.33 of a day = 5/11 of a day (since both the numerator and the denominator are divisible by 1.66), then the work will be completed in 5 5/11 days

The Concept of Negative Work

• Suppose, that A and B are working to build a wall while C is working to break the wall. In such a case, the wall is being built by A and B while it is being broken by C. Here, if we consider the work as the building of the wall, we can say that C is doing negative work

• A can build a wall in 10 days and B can build it in 5 days, while C can completely destroy the wall in 20 days. If they start working at the same time, in how many days will the work be completed

• The net combined work per day here is: A’s work + B’s work – C’s work = 10% + 20% – 5% = 25% work in one day

• Hence, the work will get completed (100% work) in 4 days

WORK EQUIVALENCE METHOD : Work rate × Time = Work done (or work to be done)

• A contractor estimates that he will finish the road construction project in 100 days by employing 50 men. However, at the end of the 50th day, when as per his estimation half the work should have been completed, he finds that only 40% of his work is done. (a) How many more days will be required to complete the work? (b) How many more men should he employ in order to complete the work in time?

• The contactor has completed 40% of the work in 50 days. If the number of men working on the project remains constant, the rate of work also remains constant. Hence, to complete 100% work, he will have to complete the remaining 60% of the work. For this he would require 75 more days

• In order to complete the work on time, it is obvious that he will have to increase the number of men working on the project

• 50 men working for 50 days then 50 × 50 = 2500 man-days

• 2500 man-days has resulted in 40% work completion. Hence, the total work to be done in terms of the number of man-days is got by using unitary method: Work left = 60% = 2500 × 1.5 = 3750 man-days

• This has to be completed in 50 days. Hence, the number of men required per day is 3750/50 = 75 men. Since, 50 men are already working on the project, the contractor needs to hire 25 more men

Work as volume of work

• In certain cases, the unit of work can also be considered to be in terms of the volume of work. For example, building of a wall of a certain length, breadth and height.

• In such cases, the following formula applies:

• L1B1H1L2B2H2=m1t1d1m2t2d2

• where L, B and H are respectively the length, breadth and height of the wall to be built, while m, t and d are respectively the number of men, the amount of time per day and the number of days. Further, the suffix 1 is for the first work situation, while the suffix 2 is for the second work situation

Q. 20 men working 8 hours a day can completely build a wall of length 200 meters, breadth 10 metres and height 20 metres in 10 days. How many days will 25 men working 12 hours a day require to build a wall of length 400 meters, breadth 10 metres and height of 15 metres.

• L1B1H1L2B2H2=m1t1d1m2t2d2

• Then we get (200 × 10 × 20)/(400 × 10 × 15) = (20 × 8 × 10)/(25 × 12 × d2)

• d2 = 8 days

Equating Men, Women and Children This is directly derived from the concept of efficiencies

• 8 men can do a work in 12 days while 20 women can do it in 10 days. In how many days can 12 men and 15 women complete the same work.

• Total work to be done = 8 × 12 = 96 man-days or total work to be done = 20 × 10 = 200 woman-days

• Since, the work is the same, we can equate 96 man-days = 200 woman-days. Hence, 1 man-day = 2.08333 woman-days

• Now, if 12 men and 15 women are working on the work we get 12 men are equal to 12 × 2.08333 = 25 women

• Hence, the work done per day is equivalent to 25 + 15 women working per day

• That is, 40 women working per day

• Hence, 40 × no. of days = 200 woman days. Number of days = 5 days

### Solved Question Papers

Q.
Raju can do 25% of a piece of work in 5 days. How many days will he take to complete the work ten times?

150
250
200
180

Ans .200

Explanation :
He will complete the work in 20 days. Hence, he will complete ten times the work in 200 days.

Q.
6 men can do a piece of work in 12 days. How many men are needed to do the work in 18 days.

3
6
4
2
Ans .4

Explanation :
6 men for 12 days means 72 mandays. This would be equal to 4 men for 18 days

Q.
Subhash can copy 50 pages in 10 hours; Subhash and Prakash together can copy 300 pages in 40 hours. In how much time can Prakash copy 30 pages?

13
12
11
9

Ans .12

Explanation :
Subhash can copy 200 pages in 40 hours (reaction to the first sentence). Hence, Prakash can copy100 pages in 40 hours. Thus, he can copy 30 pages in 30% of the time: i.e. 12 hours

Q.
X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?

10
11
12
15

Ans .12

Explanation :
30X = 20 (X + 6) = 10X = 120 = X = 12

Q.
Sashi can do a piece of work in 25 days and Rishi can do it in 20 days. They work for 5 days and then Sashi goes away. In how many more days will Rishi finish the work?

10
12
14
none

Ans .11

Explanation :
Sashi = 4%, Rishi = 5%. In five days, they do a total of 45% work. Rishi will finish the remaining
55% work in 11 more days.

Q.
A can do a piece of work in 20 days and B can do it in 15 days. How long will they take if both work together?

8 6/7
8 4/7
9 3/7
9 4/7

Ans .9 4/7

Explanation :
A’s one day work will be 5%, while B will do 6.66 % of the work in one day. Hence, their total
work will be 11.66% in a day.
In 8 days they will complete Æ 11.66 × 8 = 93.33%
This will leave 6.66% of the work. This will correspond to 4/7 of the ninth day since in
6.66/11.66 both the numerator and the denominator are divisible by 1.66.

Q.
In question 3 if C, who can finish the same work in 25 days, joins them, then how long will they take to complete the work?

6 18/47
12
2 8/11
47 6/18

Ans .6 18/47

Explanation :
A’s work = 5% per day
B’s work = 6.66% per day
C’s work = 4% per day.
Total no. of days = 100/15.66 = 300/47 = 6(18/47)

Q.
Nishu and Archana can do a piece of work in 10 days and Nishu alone can do it in 12 days. In how many days can Archana do it alone?

60
30
50
45

Ans .60

Explanation :
N + A = 10%
N = 8.33%
Hence A = 1.66% = 60 days.

Q.
Baba alone can do a piece of work in 10 days. Anshu alone can do it in 15 days. If the total wages for the work is  50. How much should Baba be paid if they work together for the entire duration of the work?

30
20
50
40

Ans .30

Explanation :
The ratio of the wages will be the inverse of the ratio of the number of days required by each to do he work. Hence, the correct answer will be 3:2 = 30

Q.
4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?

22 2/7
25 1/2
5 1/7
12 7/22

Ans .22 2/7

Explanation :
24 man days + 18 women days = 20 man days + 28 woman days
= 4 man days = 10 woman days.
= 1 man day = 2.5 woman days
Total work = 24 man days + 18 woman days = 60 woman days + 18 woman days = 78 woman
days.
Hence, 1 man + 1 woman = 3.5 women can do it in 78/3.5 = 156/7 = 22(2/7) days.

Q.
If 8 boys and 12 women can do a piece of work in 25 days, in how many days can the work be done by 6 boys and 11 women working together?

15
10
12
cant say

Ans .cant say

Explanation :
The data is insufficient, since we only know that the work gets completed in 200 boy days and 300
women days.

Q.
A can do a piece of work in 10 days and B can do the same work in 20 days. With the help of C, they finish the work in 5 days. How long will it take for C alone to finish the work?

20
10
35
15

Ans .20

Explanation :
A = 10%, B = 5% and Combined work is 20%. Hence, C’s work is 5% and will require 20 day

Q.
A can do a piece of work in 20 days. He works at it for 5 days and then B finishes it in 10 more days. In how many days will A and B together finish the work?

8
10
12
6

Ans .8

Explanation :
In 5 days, A would do 25% of the work. Since, B finishes the remaining 75% work in 10 days, we
can conclude that B’s work in a day = 7.5%
Thus, (A + B) = 12.5% per day.
Together they would take 100/12.5 = 8 days

Q.
A and B undertake to do a piece of work for  100. A can do it in 5 days and B can do it in 10 days. With the help of C, they finish it in 2 days. How much should C be paid for his contribution?

40
20
60
30

Ans .40

Explanation :
A = 20%, B = 10% and A + B + C = 50%. Hence, C = 20%. Thus, in two days, C contributes 40%
of the total work and should be paid 40% of the total amount

Q.
Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?

5
10
15
20

Ans .15

Explanation :
Total man days required = 600 man days. If 5 workers leave the job after ‘n’ days, the total work
would be done in 35 days. We have to find the value of ‘n’ to satisfy:
20 × n + (35 – n) × 15 = 600.
Solving for n, we get
20n – 15n + 35 × 15 = 600
5n = 75
n = 15.

Q.
Arun and Vinay together can do a piece of work in 7 days. If Arun does twice as much work as Vinay in a given time, how long will Arun alone take to do the work

6.33
10.5
11
72

Ans .10.5

Explanation :
Let the time taken by Arun be ‘t’ days. Then, time taken by Vinay = 2t days.
1/t + 1/2t = 1/7 = t = 10.5