Calculating percentage increase in workforce to reduce time
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
10%
(50/3)%
20%
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\%.
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
See all questions on Time & Work / Percentages
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