Three friends, Gerard, Rooney, and Ronaldson, work together to dig a hole.…
2023
Three friends, Gerard, Rooney, and Ronaldson, work together to dig a hole. Gerard alone can complete the work in 10 days, Rooney alone in 8 days, and all three together can complete it in 4 days. They earn a total of Rs. 1,200. If the money is divided in proportion to the work each person does, find Rooney's share.
Answer: D. Rs. 600 — Concept: When several people work together and are paid in proportion to the work each contributes, the payment ratio equals the ratio of their individual…
- A.
Rs. 480
- B.
Rs. 165.51
- C.
Rs. 500
- D.
Rs. 600
Attempted by 5 students.
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Correct answer: D
Concept: When several people work together and are paid in proportion to the work each contributes, the payment ratio equals the ratio of their individual work rates (rate = 1/time taken alone), not the ratio of their individual times.
Gerard's work rate = 1/10 work per day.
Rooney's work rate = 1/8 work per day.
Combined rate of all three working together = 1/4 work per day.
So Ronaldson's rate = 1/4 − 1/10 − 1/8. Taking LCM 40: 10/40 − 4/40 − 5/40 = 1/40 work per day.
Ratio of individual rates, Gerard : Rooney : Ronaldson = 1/10 : 1/8 : 1/40 = 4 : 5 : 1 (multiplying through by 40).
Sum of ratio parts = 4 + 5 + 1 = 10, so Rooney's share of the ratio is 5/10.
Rooney's share = 5/10 × Rs. 1,200 = Rs. 600.
Cross-check: Gerard gets 4/10 × 1200 = Rs. 480, Rooney gets Rs. 600, and Ronaldson gets 1/10 × 1200 = Rs. 120. Sum = 480 + 600 + 120 = Rs. 1,200, matching the given total — confirming the split is correct.