Multiple choice

Two persons Aman and Bhanu can dig a pit in 20 days and 25 days respectively and a third person Cheenu can fill that pit in 50 days. All of the three persons start their work and after sometime Cheenu leaves the work. If total time taken to dig the pit from the beginning is 13 days, find after how many days Cheenu left his work?

  1. 8.5 days

  2. 7.5 days

  3. 9.5 days

  4. 8 days

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

Aman rate = 1/20, Bhanu = 1/25, Cheenu = -1/50. Let t be the time Cheenu worked. (1/20 + 1/25 - 1/50)t + (1/20 + 1/25)(13-t) = 1. (5/100 + 4/100 - 2/100)t + (9/100)(13-t) = 1. 0.07t + 1.17 - 0.09t = 1. 0.17 = 0.02t. t = 8.5 days.

AI explanation

The one-day work of Aman, Bhanu and Cheenu is 1/20, 1/25 and 1/50 respectively. When all three work together, their combined one-day work is (5+4-2)/100 = 7/100 of the pit. Let Cheenu leave after x days, meaning the remaining (13-x) days involve only Aman and Bhanu, whose combined one-day work is 9/100. The total work equation is x(7/100) + (13-x)(9/100) = 1. Multiplying by 100 gives 7x + 117 - 9x = 100. Solving 2x = 17 yields x = 8.5 days.

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