Question

A and B can do a piece of work in 10 hours, B and C in 12 hour
and Sand A in 15 hours. How long will they take if they work
together? How long will cach take to complete the work
Independently?​

Answer 1

Let A, B and C each can complete the work alone in a, b and c hours respectively, so that,

• part of work done by A alone in one day = (1 / a).
• part of work done by B alone in one day = (1 / b).
• part of work done by C alone in one day = (1 / c).

Given that A and B together can complete it in 10 hours. So A and B together can complete 1 / 10 part of the work in one day. Thus,

(1 / a) + (1 / b) = 1 / 10 → (1)

Given, B and C together can complete it in 12 hours. So B and C together can complete 1 / 12 part of the work in one day. Thus,

(1 / b) + (1 / c) = 1 / 12 → (2)

Similarly, C and A together can complete it in 15 hours. So C and A together can complete 1 / 15 part of the work in one day. Thus,

(1 / c) + (1 / a) = 1 / 15 → (3)

Adding (1), (2) and (3), we get,

2[(1 / a) + (1 / b) + (1 / c)] = 1 / 4

(1 / a) + (1 / b) + (1 / c) = 1 / 8 → (4)

This means A, B and C all together can complete the work in 8 hours.

Subtracting (2) from (4),

1 / a = (1 / 8) - (1 / 12)

1 / a = 1 / 24

Thus A alone can do the work in 24 hours, i.e., one day.

Subtracting (3) from (4),

1 / b = (1 / 8) - (1 / 15)

1 / b = 7 / 120

Thus B alone can do the work in 120 / 7 hours.

Subtracting (1) from (4),

1 / c = (1 / 8) - (1 / 10)

1 / c = 1 / 40

Thus C alone can do the work in 40 hours.

#answerwithquality

#BAL