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K and L can complete a piece of work together in 15 days. K starts working and works for 10 days to complete two-fifth piece of work. L completes the remaining piece of work. The per-day wages paid to L  is Rs. 200. How much does L earn from completion of the remaining piece of work?

K and L can complete a piece of work together in 15 days. K starts working and works for 10 days to complete two-fifth piece of work. L completes the remaining piece of work. The per-day wages paid to L  is Rs. 200. How much does L earn from completion of the remaining piece of work? Correct Answer Rs. 4,500

Given:

K and L can complete a piece of work together in 15 days.

K starts working and works for 10 days to complete two-fifth piece of work.

L completes remaining piece of work.

The wages paid per day to L is Rs. 200.

Concepts used:

1 day work done by individual = Work/time

Time = Work/Efficiency

Total earnings = Wages per day × Number of working days

Calculation:

Time = Work/Efficiency

⇒ Time taken by K to complete full piece of work = 10 × 5/2 = 25 days

1 day work done by individual = Work/time

⇒ 1 day work of K = 1/25

Let L can complete the work in x days.

⇒ 1 day work of L = 1/x

K and L can complete a piece of work together in 15 days.

⇒ (1/25) + (1/x) = 1/15

⇒ 1/x = (1/15) – (1/25)

⇒ 1/x = 2/75

⇒ x = 75/2 days = 37.5 days

K completed 2/5th piece of work.

Remaining work = 1 – (2/5) = 3/5

Time taken by L to complete full work = 37.5 days

⇒ Time taken by L to complete 3/5 piece of work = (3/5) × 37.5 days = 22.5 days 

The wages paid per day to L is Rs. 200.

⇒ Total earnings of L = Rs. 200 × 22.5 = Rs. 4,500

∴ L earned Rs. 4,500 from completion of remaining 3/5th piece of work.

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