# Time and Work ( 21 to 25 )

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Time and Work ( 21 to 25 ):

# APTITUDE QUESTIONS (TIME AND WORK):

21. 5 men and 2 boys working together can do four times as much work as a man and a boy. What are the working capacities of a woman and a boy in ratio?

A) 3:2

B) 2:1

C) 4:3

D) 3:1

E) None of these

Explanation:

Let consider 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.
Then, 5x + 2y = 4(x + y) => x = 2y => x/y = 2/1

22. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days work will be completed by 10 women?

A) 40

B) 30

C) 45

D) 50

E) None of these

Explanation:

Let consider 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10
Solving these two equations, we get x = 11/400, y = 1/400
∴ 1 woman’s 1 day’s work = 1/400
10 women’s 1 day’s work = (1/400* 10) = 1/40
∴ the work will be completed by 10 women in 40 days.

23. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days. How much time will be taken by 15 men and 20 boys for doing the same type of work?

A) 4 days

B) 8 days

C) 2 days

D) 5 days

E) None of these

Explanation:

Let us consider 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y
Then, 6x + 8y = 1/10 and 26x + 48y = 1/2
By solving these two equations, we get x = 1/100 and y = 1/200
(15 men + 20 boys)’s 1 day’s work = (15/100+ 20/200) = 1/4
∴ the work will be completed by 15 men and 20 boys in 4 days.

24. A man is paid Rs.20 for each day he works and forfeits rs.3 for each day he is idle. At the end of 60 days he gets Rs.280. Then, he was idle for

A) 30 days

B) 25 days

C) 20 days

D) 40 days

E) None of these

Explanation:

Let the man was idle for x days.
∴ 20(60 – x) – 3x = 280
23x = 920
x = 40

25. ‘A’ takes twice as much time as ‘B’ or thrice as much times to finish a piece of work. If they work together than they can finish the work in 2 days. B can do the work alone in:

A) 8 days

B) 6 days

C) 4 days

D) 12 days

E) None of these

Explanation:

Let A, B and C take x, x/2 and x/3 hours respectively to finish the work.
Then, (1/x+ 2/x+ 3/x) = 1/2 => 6/x = 1/2 => x = 12
∴ B takes 6 hours to finish the work.