A man and a boy together can do a certain work in 40 days. Their work skills are in the ratio of 8 : 5. How many days will the boy take to finish the same work ?

The correct answer is (B) 104.

• Given Data & Principle: The ratio of the work skills (efficiency) of the man and the boy is given as 8 : 5. Let the man's efficiency per day be 8 units and the boy's efficiency per day be 5 units. The total combined work can be completed by both working together in 40 days.
• Step-by-Step Calculation: Combined daily work efficiency of the man and the boy = 8 + 5 = 13 units/day. Total work = (Combined efficiency) × (Total days) = 13 units/day × 40 days = 520 units. Now, to find the number of days the boy alone will take to finish the same work, divide the total work by the boy's daily efficiency: Days taken by the boy = Total work / Boy's efficiency = 520 / 5 = 104 days.
• Option Contrast: Alternative options (A) 88, (C) 108, and (D) 94 are mathematically incorrect derived from improper arithmetic operations or incorrect summation of efficiencies and do not yield the exact total work units required.