A person X can do a piece of work worth ₹3000 in 6 days. But he engages an…

Concept

Work rate is the fraction of a job completed per unit time.

When two people work together, their rates add, so an assistant’s rate equals the combined rate minus the first person’s rate. Payment for the same job is divided in proportion to each person’s contribution.

Application

1. X’s rate is 1/6 of the job per day.

2. The combined rate of X and Y is 1/4 of the job per day.

3. Therefore, Y’s rate is 1/4 − 1/6 = (3 − 2)/12 = 1/12 of the job per day.

4. In 4 days, Y completes 4 × 1/12 = 1/3 of the job.

5. Y’s share is ₹3000 × 1/3 = ₹1000.

Cross-check

In 4 days, X completes 4 × 1/6 = 2/3 of the job. The contributions 2/3 + 1/3 equal the whole job, and the corresponding shares ₹2000 + ₹1000 equal ₹3000.

Result

The assistant Y’s share is ₹1000.