Mohit started the work and left after 2 days, and the remaining work is completed by Suresh in 9 days. If Mohit left the work after 3 days, then Suresh will complete the remaining work in 6 days. In how many days Mohit and Suresh can complete the work individually?
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5, 15
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12, 15
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10, 12
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7, 14
A
Correct answer
Explanation
Let Mohit's rate = 1/M work per day, Suresh's rate = 1/S work per day. Case 1: 2/M + 9/S = 1. Case 2: 3/M + 6/S = 1. Solve the simultaneous equations. Subtract: (3/M + 6/S) - (2/M + 9/S) = 0 → 1/M - 3/S = 0 → 1/M = 3/S → S = 3M. Substitute in first equation: 2/M + 9/(3M) = 1 → 2/M + 3/M = 1 → 5/M = 1 → M = 5 days, S = 15 days. This is a classic work-rate problem with changing scenarios.