Two-person collaboration: Vandana completes the work in 10 days alone; with Ruchi, the work finishes in 6 days. If they earn ₹ 200 for the job, what is Ruchi’s fair share?

Introduction / Context:
When one worker’s solo time and the combined time are known, we can find the second worker’s rate by subtracting rates. Payment for the joint job is split according to the ratio of their rates (equivalently, their contributed fractions of the job).

Given Data / Assumptions:

• Vandana alone: 10 days ⇒ rate_V = 1/10.
• Vandana + Ruchi together: 6 days ⇒ rate_(V+R) = 1/6.
• Total payment = ₹ 200; wages proportional to work done.

Concept / Approach:
Ruchi’s rate = 1/6 − 1/10. Then compute the ratio of Vandana’s to Ruchi’s rates to split the payment. Finally, apply the ratio to ₹ 200 to extract Ruchi’s share.

Step-by-Step Solution:

Verification / Alternative check:
Vandana’s share would be ₹ 120 (3/5 of ₹ 200); the sum is ₹ 200 and matches the 3:2 ratio.

Why Other Options Are Wrong:
₹ 100, ₹ 60, and ₹ 75 do not equal 2/5 of ₹ 200; ₹ 120 is Vandana’s share, not Ruchi’s.

Common Pitfalls:
Subtracting days instead of rates, or splitting equally despite different speeds.

Final Answer:
₹ 80