Question

A and B can together do a piece of work in 15 days. If one day work of A be 1 and half times one day work of B, find in how many days, each alone will do the work.

Answer 1

30 days work A or B each alone will do the work

Answer 2

Answer:

37½ days

Step-by-step explanation:

Let A’s one day work be x and B’s one day work be y.

Then according to the first condition given in the problem, we have

x = (3/2)y

2x = 3y

2x – 3y = 0 … (i)

Also given, in 15 days: A and B together can do a piece of work

So, according to this condition we have

x + y = 1/15

15 (x + y) = 1

15x + 15y = 1 … (ii)

Multiplying equation (i) by 5, we get

10x – 15y = 0

15x + 15y = 1

——————

25x = 1

x = 1/25

On substituting the value of x in equation (i), we get

2(1/25) – 3y = 0

2/25 = 3y

y = 2/75

Therefore, Man A will do the work in 1/x days = 1/(1/25) = 25 day and Man B will do the work in (1/y) days = 1/(2/75) = 75/2 = 37½ days.