Isolating one worker’s time from group times: Ganesh, Ram, and Sohan together can do a work in 16 days. Ganesh and Ram together can do the same work in 24 days. How long will Sohan alone take to complete the work?
Aptitude
Time and Work
Difficulty: Easy
Choose an option
Answer
Correct Answer: 48 days
Explanation
Introduction / Context:Subtract the pair rate from the triple rate to isolate Sohan’s rate, then invert to get his time alone.
Given Data / Assumptions:
- G + R + S = 1/16 per day.
- G + R = 1/24 per day.
Concept / Approach:Sohan’s rate = (G + R + S) − (G + R) = 1/16 − 1/24.
Step-by-Step Solution:1/16 − 1/24 = (3 − 2)/48 = 1/48.Sohan alone time = 1 / (1/48) = 48 days.
Verification / Alternative check:Check: 1/24 + 1/48 = 1/16 ⇒ consistent.
Why Other Options Are Wrong:24, 36, 42, 40 days contradict the computed rate difference.
Common Pitfalls:Adding 16 and 24 or taking an average instead of subtracting rates.
Final Answer:48 days