# Time and Work Questions

FACTS  AND  FORMULAE  FOR  TIME  AND  WORK  QUESTIONS

1. If A can do a piece of work in n days, then A's 1 day's work =$\frac{1}{n}$

2. If A’s 1 day's work =$\frac{1}{n}$, then A can finish the work in n days.

3. A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

NOTE :

Hence,

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours = $\frac{100}{Efficiency}$

Q:

A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6 AM and they work alternately for one hour each. When will the work be completed?

 A) 4 days B) 5 days C) 6 days D) 7 days

Explanation:

Work donee by A and B in the first two hours, working alternatively = First hour A + Second hour B = (1/4) + (1/12) = 1/3.

Thus, the total time required to complete the work  = 2 (3) = 6 days

45 18951
Q:

A can finish a work in 18 days and B can do the same work in half the time taken by A. then, working together, what part of the same work they can finish in a day ?

 A) Total work B) One-fourth work C) Half work D) Two-third work

Explanation:

A can do the work = 18 days
B can do the work = 18/2 = 9 days
(A + B)'s 1 day work = 1/18 + 1/9 = 1/6
=> In 3 days = 3x1/6 = 1/2 work is completed.

30 18492
Q:

9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days ?

 A) 15 days B) 11 days C) 14 days D) 12 days

Explanation:

9M + 12B ----- 12 days ...........(1)
12M + 12B ------- 10 days........(2)
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B............(3)

From (1) & (3)

18B + 12B = 30B ---- 12 days

20B + 10B = 30B -----? => 12 days.

22 18229
Q:

When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. who is most efficient?

 A) A B) B C) C D) can't be determined

Explanation:

A + B= 70%

B + C =50%

=> B= 20%     A= 50%        and   C=30%

Hence A is most efficient

31 17398
Q:

A can do a piece of work in 30 days. He works at it for 6 days and then B finishes it in 18 days. In what time can A and B together it ?

 A) 14 1/2 days B) 11 days C) 13 1/4 days D) 12 6/7 days

Explanation:

Let 'B' alone can do the work in 'x' days

6/30 + 18/x = 1

=> x = 22.5

1/30 + 1/22.5 = 7/90

=> 90/7 = 12 6/7 days

28 17345
Q:

A contractor undertakes to complete a work in 130 days. He employs 150 men for 25 days and they complete 1/4 of the work . He then reduces the number of men to 100, who work for 60 days, after which there are 10 days holidays.How many men must be employed for the remaining period to finish the work?

150 men in 25 days do = $14$ work

Let 1 man in 1 day does = x  work

Total work done by 150 men in 25 days = 150x *  25 = $14$   work => x = $115000$

Therefore, 100 men in 60 days do = 100 * 60x = 6000x work = 6/15 = 2/5

Total work done =

Therefore, Remaining work = 1 - $1320$ = $720$

Remaining time = 130 - (25+60+10) = 35 days

Therefore, work is done in 25 days by 150 men.

Therefore, Work is done in 35 days by 150 men.

Hence, he should employ 50 more men.

16200
Q:

Amar can do a piece of work in 10 days. He works at it for 4 days and then Arun finishes it in 9 days. In how many days can Amar and Arun together finish the work ?

 A) 4 days B) 8 days C) 3 days D) 6 days

Explanation:

4/10 + 9/x = 1     => x = 15

Then both can do in

1/10 + 1/15 = 1/6     => 6 days

19 16048
Q:

A, B and C can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:

 A) 1/24 days B) 7/24 days C) 24/7 days D) 4 days