Question

A, B and C can do a work in 10, 20 and 30 days respectively. Find the time work will be finished in if B is assisted by A on every alternate day and by C on every third day.
1. 25/3
2. 26/3
3. 28/3
4. 31/3

Answer 1

Correct Answer - Option 3 : 28/3

Given:

A, B and C can do a work in 10, 20 and 30 days respectively.

Formula Used:

If A and B can together finish a work in t days and alone can finish the work in a and b days respectively,

Then, 1/a + 1/b = 1/t

Work = Time × Efficiency

Calculation:

Total work = LCM of 10, 20, 30 = 60 units

Efficiency of A = 6

Efficiency of B = 3

Efficiency of C = 2

1    2    3    4    5    6    7    8    9    10 (Days)

B  BA BC  BA  B  ABC B  AB  BC  AB

3    9   5     9     3 11     3    9    5     9

57 units can be completed in 9 days.

Remaining work = (60 – 57) units = 3 units

On 10^th day 9 units will be done

Remaining 3 units will be done in = 3/9 days = 1/3 days

Total work will be done in = (9 + 1/3) days = 28/3 days

∴ The work will be finished in 28/3 days.