Question

Akash and Bhuvan together can finish the work in 13 days. If after working for 5 days, Akash left the work and Chethan joined Bhuvan to finish the work in 6 more days. Find the time taken by Chethan to finish the work alone, given Bhuvan is twice as efficient as Akash.

1. \(19\frac{1}{2}\) days
2. \(17\frac{1}{2}\) days
3. \(15\frac{1}{2}\) days
4. \(13\frac{1}{2}\) days
5. \(21\frac{1}{2}\) days

Answer 1

Correct Answer - Option 1 : \(19\frac{1}{2}\) days

Given:

Time is taken by Akash and Bhuvan to finish the work = 13 days

Number of days after which Akash left work = 5 days

Number of days taken by Chethan and Bhuvan to finish work after Akash left = 6 days

The efficiency of Bhuvan = 2 × efficiency of Akash

Concept used:

Work = time × efficiency

Calculation:

The ratio of efficiency of Bhuvan to Akash = 2 ∶ 1

Then, total work done by both together = 13 × (2x + 1x) = 39x 

Let the efficiency of Chethan be ‘c’.

Total work = (Akash + Bhuvan) × 5 + (Chethan + Bhuvan) × 6

⇒ 39x = 3x × 5 + (c + 2x) × 6

⇒ c + 2x = 4x

Or, efficiency of Chethan = 2x

Time taken by Chethan to finish the work alone = 39x/2x = \(19\frac{1}{2}\) days.

∴ Chethan will take \(19\frac{1}{2}\) days to finish the work.