Multiple choice

P alone can complete a certain job in x days. Q alone can complete the same job in 2x day. R alone can complete the same job in (x + 32) days. Also, P and R together can complete the same job in 12 days. R starts working and works for (x/4) days. After that, P and Q join R to complete the remaining task together. Find the value of (Y + 1/2) days, if Y is the number of days taken by P, Q and R together to complete the remaining task.

  1. 8.5 days

  2. 8 days

  3. 7.5 days

  4. 9.5 days

  5. 10.5 days
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A Correct answer
Explanation

P = 1/x, Q = 1/2x, R = 1/(x+32). P+R = 1/12 => 1/x + 1/(x+32) = 1/12. (2x+32)/(x^2+32x) = 1/12 => x^2 + 32x = 24x + 384 => x^2 + 8x - 384 = 0. (x+24)(x-16) = 0. x = 16. P=1/16, Q=1/32, R=1/48. R works x/4 = 4 days. Remaining = 1 - 4/48 = 11/12. P+Q+R = 1/16 + 1/32 + 1/48 = (6+3+2)/96 = 11/96. Y = (11/12) / (11/96) = 8. Value = Y + 0.5 = 8.5.

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