Work and time - value of n
Question
X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in 8 2/3 days. What is n equal to ?
Options
3
4
5
6
Explanation
First, find the total time each takes to complete 100\% of the work: X = 6 × 3 = 18 days. Y = 8 × 3 = 24 days. Z = 12 × (4/3) = 16 days. Assume Total Work = LCM(18, 24, 16) = 144 units. Calculate daily efficiencies: X = 144/18 = 8 units/day. Y = 144/24 = 6 units/day. Z = 144/16 = 9 units/day. Combined daily work rate = 8 + 6 + 9 = 23 units/day. They work together for n days, completing 23n units. Y finishes the remainder in 82/3 days (26/3 days). Work done by Y alone = (26/3) × 6 = 52 units. Total work equation: ⟨MATH⟩23n + 52 = 144⟨/MATH⟩. 23n = 92 \implies n = 4.
Answer: (b).
Question details
Year
2025
Paper
CSAT
Question
Q49
Section
Numerical Ability
Sub-topic
Time & Work
Type
Arithmetic word problem
Difficulty
Hard
Source hint
Time-work application
Same sub-topic — other years
Time & Work has appeared in multiple CSAT papers:
Q38
2024
Determining data sufficiency for calculating a combined work rate
Q50
2024
Evaluating data sufficiency for determining total work output
Q20
2023
Alternating time and work schedule (A, B, C)
Q57
2022
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