Multiple choice

Kirti and Sham can do a piece of work in 30 days and 25 days, respectively. Kirti started the work alone and then after 7 days, Sham joined her till the completion of the work. How long did the work last?

  1. 17.18 days

  2. 20 days

  3. 18.45 days

  4. 17.45 days

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kirti's rate = 1/30, Sham's rate = 1/25. Kirti works for 7 days alone: 7/30 done. Remaining = 23/30. Together, rate = 1/30 + 1/25 = 11/150. Time taken together = (23/30) / (11/150) = (23/30) * (150/11) = 115/11 = 10.45 days. Total time = 7 + 10.45 = 17.45 days.

AI explanation

Using the least common multiple method, let the total work be 150 units, making the daily work of Kirti 5 units and the daily work of Sham 6 units. Kirti works alone for 7 days to complete 35 units, leaving 115 units of work. When they work together their combined daily capacity is 11 units, so they need 115 divided by 11 days to finish the remaining work. The total time is 7 plus 10.45 days, resulting in 17.45 days.

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