Question

Ratio of work efficiencies of A, B and C is 9 : 10 : 12 and they can finish a particular wok working together is 3 days. What is the ratio of the time required if they worked individually?
1. 20 : 18 : 15
2. 20 : 15 : 18
3. 20 : 18 : 16
4. 18 : 16 : 15
5. None of these

Answer 1

Correct Answer - Option 1 : 20 : 18 : 15

Given:

Ratio of efficiency of A, B and C = 9 : 10 : 12

Time taken by them to finish the job working together = 3 days

Formula used:

Total work = work done rate × time

Calculations:

Let us assume, efficiencies of A, B and C are 9x, 10x and 12x respectively.

Working together, amount of work done by them/day = (9x + 10x + 12x) = 31x

Total work = 31x × 3 = 93x

If A works alone, time required to finish = 93x/9x = 31/3 days

If B works alone, time required to finish = 93x/10x = 93/10 days

If C works alone, time required to finish = 93x/12x = 93/12 days

Required ratio = 31/3 : 93/10 : 93/12 = 1/3 : 3/10 : 3/12 = 20 : 18 : 15