Multiple choice

Dinesh alone can do a piece of work in 6 days while Sachin alone can do the same piece of work in 12 days. They both start working together. If Sachin leaves when half of the work is done, then how many more days will Dinesh take to complete the remaining work?

  1. 2

  2. 3

  3. 4

  4. 5

  5. 8
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B Correct answer
Explanation

Dinesh's rate is 1/6 work/day and Sachin's is 1/12 work/day. Together, their rate is 1/6 + 1/12 = 3/12 = 1/4 work/day. They complete half the work (1/2) in (1/2) / (1/4) = 2 days. The remaining 1/2 work is done by Dinesh alone at 1/6 rate, taking (1/2) / (1/6) = 3 days.

AI explanation

Using the least common multiple method, let the total work be the LCM of 6 and 12, which is 12 units. Dinesh's work rate is 12 divided by 6, equaling 2 units per day, while Sachin's work rate is 12 divided by 12, equaling 1 unit per day. Their combined rate is 3 units per day, so they complete the half-work mark of 6 units in 2 days. The remaining work is 6 units, which Dinesh completes alone at his rate of 2 units per day, requiring 3 more days.

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