Multiple choice

Avinash, Biren and Chandu can complete a piece of work. Avinash and Biren together can finish the work in 16 days, while Biren and Chandu together can finish the same work in 24 days. Initially, Avinash and Biren start the work together. Avinash works for 4 days and then leaves. Biren continues and works for a total of 6 days from the start and then leaves. After that, Chandu completes the remaining work alone in the next 34 days. In how many days can Avinash and Chandu together complete the entire work?

  1. 8

  2. 10

  3. 12

  4. 16

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let rates be A, B, C. A+B = 1/16, B+C = 1/24. Avinash works 4 days, Biren 6 days, Chandu 34 days. 4A + 6B + 34C = 1. Since A+B=1/16, 4(A+B) + 2B + 34C = 1 => 4/16 + 2B + 34C = 1 => 2B + 34C = 3/4. Since B+C=1/24, 2(B+C) + 32C = 3/4 => 2/24 + 32C = 3/4 => 32C = 3/4 - 1/12 = 8/12 = 2/3. C = 2/96 = 1/48. B = 1/24 - 1/48 = 1/48. A = 1/16 - 1/48 = 2/48 = 1/24. A+C = 1/24 + 1/48 = 3/48 = 1/16. Time = 16 days.

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