Abhishek and Deepanshi undertake to do a piece of work for ₹1,000. Abhishek alone can do it in 5 days and Deepanshi alone can do it in 10 days. With the help of Chitransh, they finish it in 2 days. How much should Chitransh be paid for his contribution?

Given:

Total payment for the work = ₹1,000

Abhishek alone can do the work in 5 days

Deepanshi alone can do the work in 10 days

Abhishek, Deepanshi, and Chitransh together finish the work in 2 days

Formula used:

Efficiency = Total Work / Time taken

Payment shared in the ratio of efficiencies.

Calculations:

Let the total work be the LCM of 5, 10, and 2.

LCM(5, 10, 2) = 10 units

Abhishek's efficiency = 10 units / 5 days = 2 units/day

Deepanshi's efficiency = 10 units / 10 days = 1 unit/day

Combined efficiency of Abhishek, Deepanshi, and Chitransh = 10 units / 2 days = 5 units/day

Chitransh's efficiency = Combined efficiency - Abhishek's efficiency - Deepanshi's efficiency

⇒ Chitransh's efficiency = 5 units/day - 2 units/day - 1 unit/day = 2 units/day

The ratio of their efficiencies (work done) = Abhishek : Deepanshi : Chitransh

⇒ Ratio = 2 : 1 : 2

Total parts in the ratio = 2 + 1 + 2 = 5 parts

Chitransh's share of the payment = (Chitransh's efficiency / Total efficiency) × Total payment

⇒ Chitransh's share = (2 / 5) × â‚¹1,000

⇒ Chitransh's share = 2 × â‚¹200

⇒ Chitransh's share = ₹400

∴ The correct answer is option 4.