P and Q can do a job in 24 days, Q and R can do it in 30 days, while P and R can do it in 40 days. X is four times as efficient as P, Y is half as efficient as Q, and Z is 2.5 times as efficient as R. Determine the number of days required to complete the same job if X , Y and Z work together.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 10.
Given:
P and Q can do a job in 24 days,
Q and R can do it in 30 days,
P and R can do it in 40 days
Calculations:
Total work (LCM of 24, 30, 40) = 120 units
The combined efficiency of P and Q = 120/24 = 5
The combined efficiency of Q and R = 120/30 = 4
The combined efficiency of P and R = 120/40 = 3
The total efficiency of P + Q + R = (5 + 4 + 3)/2 = 12/2 = 6
Now, the efficiency of P = 6 - 4 = 2
The efficiency of Q = 6 - 3 = 3
The efficiency of R = 6 - 5 = 1
X is four times as efficient as P, Y is half as efficient as Q, and Z is 2.5 times as efficient as R
⇒ X = 4 × 2 = 8
⇒ Y = 3/2 = 1.5
⇒ Z = 2.5 × 1 = 2.5
Required time taken by X + Y + Z = 120/(8 + 1.5 + 2.5) = 120/12 = 10