7. 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?

1. A. 10%
2. B. (50/3)%
3. C. 20%
4. D. 25%

Answer: C

Explanation

This is a classic inverse proportionality problem in time and work. The total amount of work is constant. We know that Work = Number of Men × Number of Days. Let the initial number of men be M1 and the initial number of days be D1 = 6k. Let the new number of men be M2 and the new number of days be D2 = 5k. Since the work is the same, M1 × D1 = M2 × D2. Substituting the values: M1 × 6k = M2 × 5k. This simplifies to 6M1 = 5M2, or M2 = (6/5)M1. To find the percentage increase in the number of men: Percentage Increase = ((M2 – M1) / M1) × 100 = (((6/5)M1 – M1) / M1) × 100 = ((1/5)M1 / M1) × 100 = (1/5) × 100 = 20%. Thus, the number of men needs to be increased by 20%. This question tests basic proportionality and percentage calculations.