Time and Work
Q1

12 man can do a piece of work in 25 days.How long will 10 men take to complete the work?

Ans: 12 X 25 / 10 = 30

Q2

30 man can do a piece of work in 36 days.What is the number of men needed to complete the same work in 24 days?

Ans: 30 X 36 / 24 = 45

Q3

12 man can do a piece of work in 18 days.What is the extra number of men needed to complete the same work in 8 days?

Ans: The number of men needed to complete the work in 8 days = 12 X 18 / 8 = 27
Number of men needed extra = 27 - 12 = 15

Q4

80 man can do a piece of work in 90 days.If 20 more men joined with them how long will take to complete the work?

Ans: 80 X 90 / (80+20) = 72 days

Q5

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is ?

Ans:

 A's 1 day's work = 1 ; 15
 B's 1 day's work = 1 ; 20
 (A + B)'s 1 day's work = 1 + 1 = 7 . 15 20 60

 (A + B)'s 4 day's work = 7 x 4 = 7 . 60 15
 Therefore, Remaining work = 1 - 7 = 8 . 15 15

Q6

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

Ans:

 (A + B + C)'s 1 day's work = 1 , 4
 A's 1 day's work = 1 , 16
 B's 1 day's work = 1 . 12
 C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 5 . 4 16 12 4 48 48
 So, C alone can do the work in 48 = 9 3 days. 5 5

Q7

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, the time taken by 15 men and 20 boys in doing the same type of work will be:

Ans:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

 Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2
 Solving these two equations, we get : x = 1 and y = 1 . 100 200
 (15 men + 20 boy)'s 1 day's work = 15 + 20 = 1 . 100 200 4

15 men and 20 boys can do the work in 4 days.

Q8

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

Ans:

 A's 1 hour's work = 1 ; 4
 (B + C)'s 1 hour's work = 1 ; 3
 (A + C)'s 1 hour's work = 1 . 2
 (A + B + C)'s 1 hour's work = 1 + 1 = 7 . 4 3 12
 B's 1 hour's work = 7 - 1 = 1 . 12 2 12

B alone will take 12 hours to do the work.