Work Rates — Isolating One Worker's Time from Group Data Ram, Dilip, and Shekhar together complete a job in 20 days. Ram and Dilip together complete the same job in 30 days. How many days would Shekhar alone take to complete the job?

Introduction / Context:
This problem focuses on separating one worker’s contribution from group performance. By converting times to rates and subtracting the pair’s rate from the trio’s rate, we can find Shekhar’s rate and hence his time alone.

Given Data / Assumptions:

• (Ram + Dilip + Shekhar) time = 20 days.
• (Ram + Dilip) time = 30 days.
• Constant work rates throughout.

Concept / Approach:
Rate = 1/time. Let total work = 1 job. Then r_total = 1/20 and r_RD = 1/30. Shekhar's rate r_S = r_total − r_RD. Finally, time_S = 1/r_S.

Step-by-Step Solution:
r_total = 1/20 job/dayr_RD = 1/30 job/dayr_S = 1/20 − 1/30 = (3 − 2)/60 = 1/60 job/dayShekhar's time = 1 / (1/60) = 60 days

Verification / Alternative check:
In 60 days Shekhar does exactly 1 job. Group minus pair equals the single worker’s rate; arithmetic checks out.

Why Other Options Are Wrong:
62, 56, 50, and 40 days do not align with r_S = 1/60 derived from the rates difference.

Common Pitfalls:
Subtracting times instead of rates, or mixing up which figure represents the trio vs. the pair.

Final Answer:
60 days