Shantanu completes five-eighths (5/8) of a job in 20 days at a constant pace. At this rate, how many more days are needed to finish the remaining work?

Introduction: When a fraction of work is completed in a given time at constant rate, we can derive the worker’s rate and project the time for the remaining fraction. This is a direct proportionality: time is proportional to the fraction of work at a fixed rate.

Given Data / Assumptions:

• Fraction completed: 5/8 in 20 days.
• Constant work rate throughout.
• Remaining fraction = 3/8.

Concept / Approach: Rate r = (work done) / (time) = (5/8) / 20 = 1/32 job per day. Remaining time = (remaining work)/(rate). Compute and convert to days as an integer if it divides exactly (it does here).

Step-by-Step Solution:

Verification / Alternative check: Proportion: If 5/8 takes 20 days, then 1/8 takes 4 days (divide by 5). Hence 3/8 takes 12 days (multiply by 3). Same result, quicker mental check.

Why Other Options Are Wrong: 6, 5, 8, 18 days do not match the linear scaling implied by a constant rate from 5/8 in 20 days.

Common Pitfalls: Adding times incorrectly or confusing the completed fraction with the remaining one. Always compute the residual fraction carefully.

Final Answer: 12 days