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Q7·CSAT · Prelims 2024

Calculating percentage increase in workforce to reduce time

NumericalTime & Work / PercentagesFactual singleMedium

Question

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?

Options

a

10%

b

(50/3)%

c

20%

Answer
d

25%

Explanation

Total work is the product of the number of men (M) and the number of days (D). Since total work remains constant: M_1 × D_1 = M_2 × D_2

Given D_1 = 6k and D_2 = 5k[cite: 1074, 1075]: M_1 × 6k = M_2 × 5k \implies M_2 = 6/5M_1

The fraction increase in workforce is: \Delta M = M_2 - M_1/M_1 = 6/5M_1 - M_1{M_1} = 1/5

Converting to a percentage: 1/5 × 100 = 20\%.

For constant work, workforce and timeframe are inversely proportional. Dropping time from 6 to 5 means workforce scales by 6/5, a 20\% increase.

Answer: (c).

Question details

Year

2024

Paper

CSAT

Question

Q7

Section

Numerical Ability

Sub-topic

Time & Work / Percentages

Type

Factual single

Difficulty

Medium

Source hint

Percent increase of men to complete work in 5k days instead of 6k days

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