Multiple choice

Mahesh and Umesh can complete a piece of work in 10 days and 15 days, respectively. Umesh starts the work and after 5 days, Mahesh also joins him. In how many days will the work be completed?

  1. 7 days

  2. 9 days

  3. 11 days

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Umesh does 1/15 of the work per day, Mahesh does 1/10. Umesh works alone for 5 days, completing 5/15 = 1/3 of the work. Remaining work is 2/3. Together they do 1/15 + 1/10 = 5/30 = 1/6 of the work per day. Time to finish remaining work is (2/3) / (1/6) = 4 days. Total time = 5 + 4 = 9 days.

AI explanation

Let the total work be the least common multiple of 10 and 15, which is 30 units. Umesh's efficiency is 2 units per day and Mahesh's efficiency is 3 units per day. Umesh works alone for 5 days to complete 10 units, leaving 20 units of work. When Mahesh joins, their combined efficiency is 5 units per day, so they finish the remaining 20 units in 4 days. The total time taken to complete the work is 5 plus 4, which equals 9 days.

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