Time, Work, Speed & Distance› Time & Work, Pipes & Cisterns
Mahesh and Krishna are engaged to do a work. Mahesh working alone takes 8 hours more to complete the job than if both worked together. If Krishna worked alone, he would need 4 1/2 hours more to complete the job than if they both worked together. How much time would they both take to do the work together ?
Answer d.
The answer is (d), 6 hours. If both take T hours together, then T squared equals 8 times 4.5, so T is 6. Let both working together take T hours. Then Mahesh alone takes T + 8 hours and Krishna alone takes T + 4.5 hours. Their combined rate must equal the rate of the pair: 1/(T+8) + 1/(T+4.5) = 1/T. Combine the left side: (2T + 12.5) / ((T+8)(T+4.5)) = 1/T. Cross-multiply: T(2T + 12.5) = (T+8)(T+4.5) = T² + 12.5T + 36. So 2T² + 12.5T = T² + 12.5T + 36, which gives T² = 36 and T = 6. Check: Mahesh alone takes 14 hours and Krishna alone takes 10.5 hours. 1/14 + 1/10.5 = 3/42 + 4/42 = 7/42 = 1/6. Shortcut: when the two solo times are T + a and T + b, the joint time is the square root of a times b. Here the root of 8 × 4.5 = 36 is 6.
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