Question
Download Solution PDFP 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Concept used:
Efficiency = (Total work / Total time taken)
Efficiency = work done in a single day
Calculation:
Let total work is 120 units ( LCM of 24, 30 , and 40 and)
The efficiency of P+Q = 120 /24
⇒ 5 units
The efficiency of Q+R = 120 / 30
⇒ 4 units
The efficiency of P+R = 120 / 40
⇒ 3 units
Total efficiency of P + Q + R is (4+ 5 + 3) / 2 = 6
The efficiency of P is 6 - 4 = 2 units
The efficiency of X is 2 × 4 = 8 units
The efficiency of Q is 6 - 3 = 3 units
The efficiency of Y is 3 × .5 = 1.5 units
The efficiency of R is 6 - 5 = 1 unit
The efficiency of Z is 1 × 2.5 = 2.5 units
Total efficiency of X + Y + Z is (8+ 1.5 + 2.5) = 12 units
The number of days required to complete the same job if X, Y and Z work together is,
120 /12 = 10days
∴ The correct option is 4
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