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?
Answer: D. 24 — 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.…
- A.
10
- B.
12
- C.
18
- D.
24
Attempted by 533 students.
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:
(X - 8)/36 + (X - 12)/54 + X/72 = 1
Multiply both sides by the LCM 216 to clear denominators: 6(X - 8) + 4(X - 12) + 3X = 216
Expand and combine like terms: 6X - 48 + 4X - 48 + 3X = 216 => 13X - 96 = 216
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.