A and B complete a work in 2 days. If A alone can do it in 4 days then, B alone can do 20-times of the same wo

Question

A and B complete a work in 2 days. If A alone can do it in 4 days then, B alone can do 20-times of the same work in ______________(days).

Examoogle · Accepted Answer

The correct answer is Option C: 80. Use the work efficiency formula: If (A+B) takes 'x' days and A takes 'y' days, B takes (x*y)/(y-x) days. Here (2*4)/(4-2) = 4 days. Multiply by 20 for 20-times work.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the work efficiency formula: If (A+B) takes 'x' days and A takes 'y' days, B takes (x*y)/(y-x) days. Here (2*4)/(4-2) = 4 days. Multiply by 20 for 20-times work.

Formula Used: $$\frac{1}{B} = \frac{1}{A+B} - \frac{1}{A}$$

Given: Work done by (A + B) in 2 days. Work done by A alone in 4 days.

Steps: Calculate B's work rate: Given A and B do the work in 2 days ($1/2$ per day) and A does it in 4 days ($1/4$ per day). Subtracting A's rate from the combined rate gives B's rate.. Calculate time for 1 unit of work: Since B's rate is $1/4$ of the work per day, B completes 1 unit of work in 4 days.. Calculate time for 20-times the work: If B takes 4 days for 1 unit, B takes $4 	imes 20$ days for 20 units.

Answer: C is correct because the daily work rate of B is 1/4, meaning B takes 4 days for one unit of work and 80 days for 20-times the work.

Exam Tip: This logic is identical to pipe and cistern problems where A and B represent different inlet/outlet rates.

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