Multiple choice

Ramesh and Suresh together can complete a piece of work in 24 days. Suresh and Mahesh together can complete the same work in 16 days. Mahesh and Ramesh together can complete the same work in 12 days. How long would Suresh take to complete the same task working alone?

  1. 96 days

  2. 78 days

  3. 108 days

  4. 88 days

  5. 72 days
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A Correct answer
Explanation

Let R, S, M be rates. R+S = 1/24, S+M = 1/16, M+R = 1/12. Adding them: 2(R+S+M) = 1/24 + 1/16 + 1/12 = (2+3+4)/48 = 9/48 = 3/16. So R+S+M = 3/32. To find S, subtract (M+R): S = 3/32 - 1/12 = (9-8)/96 = 1/96. Suresh takes 96 days.

AI explanation

Let the total work be 48 units, making the combined efficiencies of Ramesh and Suresh 2 units per day, Suresh and Mahesh 3 units per day, and Mahesh and Ramesh 4 units per day. Adding these three efficiencies gives 2R plus 2S plus 2M equals 9 units per day, so the combined efficiency of all three is 4.5 units per day. Subtracting the combined rate of Mahesh and Ramesh, which is 4 units per day, leaves Suresh with an efficiency of 0.5 units per day. The time Suresh takes working alone is 48 units divided by 0.5 units per day, which equals 96 days.

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