CSAT 2024 Solutions - A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?

Q7. A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?

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A. 10%

B. (50/3)%

C. 20%

D. 25%

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Answer: C. 20%

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Let the number of men required to complete the work in 6k days be denoted by m.

According to the problem, this number of men can complete the work in 6k days.

The relationship between the number of men and the time taken to complete the work can be described by the formula:

Men × Time = Work (constant)

So, initially:

m × 6k = constant work

Let the new number of men be n.

According to the formula, for the work to be completed in 5k days:

n × 5k = constant work

Since the work is constant, we can equate the two expressions for the work:

m × 6k = n × 5k

Simplifying this:

n = 6/5 × m

Percent increase = (n - m) / m × 100 = ((6/5)m - m) / m × 100 = (1/5) × 100 = 20%

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Thus, the number of men should be increased by **20%** to complete the work in 5k days.