Question
Download Solution PDFP works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q, and R together work on a job, in what ratio should they share the earnings?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
P works thrice as fast as Q.
P and Q together work four times as fast as R.
We need to find the ratio of earnings of P, Q, and R when they work together.
Formula used:
Work done ∝ Efficiency
Let the efficiency of Q = x.
Then, efficiency of P = 3x (since P works 3 times as fast as Q).
Efficiency of P + Q = 4 × Efficiency of R.
Efficiency ratio = Earnings ratio (as earnings are proportional to work done).
Calculation:
Let efficiency of Q = x.
⇒ Efficiency of P = 3x.
⇒ Efficiency of P + Q = 3x + x = 4x.
Given, Efficiency of P + Q = 4 × Efficiency of R.
⇒ 4x = 4 × Efficiency of R.
⇒ Efficiency of R = x.
Now, total efficiency of P, Q, and R when working together:
⇒ Total Efficiency = Efficiency of P + Efficiency of Q + Efficiency of R.
⇒ Total Efficiency = 3x + x + x = 5x.
Ratio of earnings = Ratio of efficiencies:
⇒ Earnings Ratio of P : Q : R = 3x : x : x = 3 : 1 : 1
∴ The correct answer is option (1).
Alternate MethodCalculation:
P works 3 times as fast as Q.
P and Q together are 4 times as fast as R.
Q's 1 day work = 1 unit
⇒ P's 1 day work = 3 units
⇒ P + Q = 3 + 1 = 4 units/day
Given P + Q = 4 × R
⇒ 4 = 4 × R
⇒ R = 1 unit/day
Work Rates:
P = 3, Q = 1, R = 1
Total work = 3 + 1 + 1 = 5 units
∴ The earnings ratio = P : Q : R = 3 : 1 : 1
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