A and B can complete a piece of work in 10 days and 15 days respectively,
Let total work be 60 units,
⇒ 1-day work of A = 6 units
⇒ 1-day work of B = 4 units
B starts the work and is joined by A after 5 days,
⇒ Work done by B in 5 days = 20 units,
⇒ Remaining work = 40 units which is done be A and B in the ratio of their efficiency

Question

Answer

Given information:

A can complete a piece of work in 10 days.

B can complete a piece of work in 15 days.

B starts the work and is joined by A after 5 days.

They earn a total of Rs. 60.

Approach:

We need to find the individual shares of A and B. To solve this problem, we can use the concept of work done by each person.

Solution:

Let's assume the total work to be done is 150 units (LCM of 10 and 15).

A's work efficiency = Total work / A's time = 150 / 10 = 15 units/day.

B's work efficiency = Total work / B's time = 150 / 15 = 10 units/day.

Work done by B in 5 days = B's work efficiency * 5 = 10 * 5 = 50 units.

Remaining work = Total work - Work done by B = 150 - 50 = 100 units.

A and B work together for the remaining 100 units of work.

Total time taken by A and B working together = Remaining work / (A's work efficiency + B's work efficiency) = 100 / (15 + 10) = 100 / 25 = 4 days.

Since B started the work 5 days earlier, the total time taken by B = 5 + 4 = 9 days.

Total time taken by A = 5 + 4 = 9 days.

A's share = (A's work efficiency * A's time) / Total time taken = (15 * 9) / 9 = 15 units.

B's share = (B's work efficiency * B's time) / Total time taken = (10 * 9) / 9 = 10 units.

To find the individual shares in terms of money, we can use the ratio of work done.

A's share in money = (A's work done / Total work) * Total money = (15 / 150) * 60 = Rs. 6.

B's share in money = (B's work done / Total work) * Total money = (10 / 150) * 60 = Rs. 4.

Therefore, A's share = Rs. 6 and B's share = Rs. 4, which is equivalent to Rs. 24 and Rs. 36 respectively. Hence, option A is the correct answer.

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