### Question 6

SSC-CGL 2019 June 13 Shift 1

The efficiencies of A, B and C are in the ratio of 5 : 3 : 2. Working together, they can complete a task in 21 hours. In how many hours will B alone complete 40% of that task?

- 28
- 24
- 35
- 21

### Solution in Short

1 hour work of A + B + C together = 5k + 3k + 2k = 10k. They take 21 hours. So total work = 21 x 10k = 210k. B has to complete 40% of 210k = 84k.

B can complete 3k in 1 hour. Hence 84k will be completed in 84k/3k = 28 hours answer!

### Solution in Detail

EXPLANATION: efficiency means "the amount of work done in 1 hour". Ratios are given so we should say that A completes 5k work in one hour, B completes 3k, and likewise C completes 2k work.Work in 1 hour by A+B+C = 5 + 3 + 2 = 10

Given that A+B+C work for 21 hours

$\displaystyle \implies$ total work = $\displaystyle 21 \times 10 = 210$

B has to complete $\displaystyle 40\% \text{ of } 210 = 84$

Efficiency of B given as = 3

$\displaystyle \implies $3 units can be done in 1 hour

By unitary method:

$\displaystyle \therefore $ 84 units can be done in $\displaystyle \frac{1}{3} \times 84$ hour

= 28 hours Answer!

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