Mr.P, Mr.Q and Mr.R takes a project and they can complete in 36 hours, 54…

2024

Mr.P, Mr.Q and Mr.R takes a project and they can complete in 36 hours, 54 hours and 72 hours respectively. Unfortunately Mr.P met an accident and left from the project 8 hours before the completion while Mr.Q left 12 hours before the completion. Then for how many hours did Mr.r worked?

  1. A.

    10

  2. B.

    12

  3. C.

    18

  4. D.

    24

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Show answer & explanation

Correct answer: D

Let the total time taken to complete the project be X hours.

Then Mr. P worked for X - 8 hours, Mr. Q worked for X - 12 hours, and Mr. R worked for X hours.

Work rates: Mr. P = 1/36 of the project per hour, Mr. Q = 1/54 per hour, Mr. R = 1/72 per hour.

Set up the equation for total work = 1:

  1. (X - 8)/36 + (X - 12)/54 + X/72 = 1

  2. Multiply both sides by the LCM 216 to clear denominators: 6(X - 8) + 4(X - 12) + 3X = 216

  3. Expand and combine like terms: 6X - 48 + 4X - 48 + 3X = 216 => 13X - 96 = 216

  4. Solve for X: 13X = 312 => X = 24

Therefore Mr. R worked for 24 hours.

Quick check: (24-8)/36 + (24-12)/54 + 24/72 = 16/36 + 12/54 + 24/72 = 4/9 + 2/9 + 1/3 = (4+2+3)/9 = 9/9 = 1.

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