Ansh and Tanvi can do a piece of work in 24 days and 40 days, respectively. They started the work, and after 8

Question

Ansh and Tanvi can do a piece of work in 24 days and 40 days, respectively. They started the work, and after 8 days, Shubham, who can complete the same work in 20 days alone, joined them. In how many days can the whole work be completed?

Examoogle · Accepted Answer

The correct answer is Option A: 16 days. Use LCM of 24, 40, 20 as 120 units. Ansh's efficiency is 5, Tanvi's is 3, Shubham's is 6. After 8 days of (5+3)=8 units/day, 64 units are done. Remaining 56 units are done by (5+3+6)=14 units/day in 4 more days. Total = 8+4 = 12 days.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use LCM of 24, 40, 20 as 120 units. Ansh's efficiency is 5, Tanvi's is 3, Shubham's is 6. After 8 days of (5+3)=8 units/day, 64 units are done. Remaining 56 units are done by (5+3+6)=14 units/day in 4 more days. Total = 8+4 = 12 days.

Formula Used: $$Total Work = LCM(24, 40, 20) = 120 units$$ $$Efficiency = \frac{Work}{Time}$$

Given: Ansh takes 24 days, Tanvi takes 40 days. They work together for 8 days, then Shubham (who takes 20 days alone) joins.

Steps: Calculate LCM and Efficiencies: Assume total work as LCM(24, 40, 20) = 120. Efficiencies are Ansh=5, Tanvi=3, Shubham=6.. Calculate work done in first 8 days: Ansh and Tanvi work together for 8 days at a rate of 5 + 3 = 8 units/day.. Calculate remaining work and time with Shubham: Remaining work is 120 - 64 = 56. With Shubham, total efficiency is 5 + 3 + 6 = 14 units/day.. Total time calculation: Adding the initial 8 days and the final 4 days.

Answer: C is correct because the total work takes 8 + 4 = 12 days to complete.

Exam Tip: This is a standard work-time variation; always define total work as the LCM of time taken by individual workers to simplify fractions.

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