A and B can do a work in 20 days. When A works at 60% capacity, B has to work at 150% capacity to finish the work. Find in how many days the faster one will finish the work alone.

Question

Given below are two statements:
Statement I: Ram and Shyam can finish a task by working together in 6 days. If Shyam can finish the task by working alone in 8 days, then Ram alone will take 24 days to finish it.
Statement II: If 6 persons working 8 hours a day earn 8,400 per week, then 9 person working 6 hours a day will eam 9,450 per week.
In the light of the above statements, choose the correct answer from the options given below:

Answer 1

Let x represent the number of days required for the faster individual (assumed to be A) to complete the work independently.

When A operates at 60% capacity and B operates at 150% capacity, their combined work rate is equivalent to \( \frac{3}{5} + \frac{3}{2} \) of the standard capacity.

The equation \( (\frac{3}{5}+\frac{3}{2}).\frac{1}{x}=\frac{1}{20} \) is established based on the premise that A and B, working collaboratively, can complete the task in 20 days.

The solution to this equation yields x=36.

Consequently, the faster individual (A) will complete the work independently in 36 days.

A and B can do a work in 20 days. When A works at 60% capacity, B has to work at 150% capacity to finish the work. Find in how many days the faster one will finish the work alone.

Solution and Explanation

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