Krishna can do a work in 10 days; Mohan can do the same in 20 days. They start together; after 3 days Krishna leaves and Mohan finishes the job alone. By how many days did Mohan's solo work exceed the total time that would have been required if both had worked together for the entire job?

Introduction / Context:This compares Mohan’s solo period (after Krishna leaves) to the full duration if both had worked together from start. Compute remaining work after 3 joint days, then Mohan’s solo time, and subtract the “together-from-start” time.

Given Data / Assumptions:

• Krishna rate = 1/10 job/day.
• Mohan rate = 1/20 job/day.
• Worked together for first 3 days; then Mohan alone.

Concept / Approach:Let RT = combined rate = 1/10 + 1/20 = 3/20 job/day. Work done in first 3 days = 3 * (3/20) = 9/20. Remainder = 11/20. Mohan alone needs (11/20)/(1/20) days. Compare this solo duration to the time needed if both had done the entire work together (which is 1 / (3/20)).

Step-by-Step Solution:

Verification / Alternative check:Compute total actual duration: 3 + 11 = 14 days. The comparison baseline (both together entire time) is 6 2/3 days; the excess in Mohan’s solo period beyond that baseline equals 4 1/3 as derived.

Why Other Options Are Wrong:3 1/4, 23/5, 3 2/3, 4 1/2 do not match the exact fraction 13/3.

Common Pitfalls:Comparing against the initial 3 days instead of “together-from-start”; forgetting to convert to a common baseline.

Final Answer:4 1/3