Three individuals X, Y, Z hired a car on a sharing basis and paid Rs. 1,040.…
2009
Three individuals X, Y, Z hired a car on a sharing basis and paid Rs. 1,040. They used it for 7, 8, 11 hours, respectively. What are the charges paid by Y ?
Answer: B. Rs. 320 — Concept. When a single fixed cost is shared in proportion to how much each person uses a resource, the cost behaves as a constant rate per unit of usage: rate…
- A.
Rs. 290
- B.
Rs. 320
- C.
Rs. 360
- D.
Rs. 440
Attempted by 43 students.
Show answer & explanation
Correct answer: B
Concept. When a single fixed cost is shared in proportion to how much each person uses a resource, the cost behaves as a constant rate per unit of usage: rate = total cost ÷ total usage, and every user pays that same rate multiplied by their own usage. Equivalently, each user's payment is the total cost times the fraction their usage forms of the combined usage, so the payments stand in exactly the same ratio as the usages.
Applying it here.
Combined usage = 7 + 8 + 11 = 26 hours, so the three payments must stand in the ratio 7 : 8 : 11.
Rate per hour = Rs. 1,040 ÷ 26 = Rs. 40 per hour.
Y used the car for 8 hours, so Y pays 8 × Rs. 40 = Rs. 320. The fraction route gives the same value: (8/26) × 1,040 = (4/13) × 1,040 = Rs. 320.
Cross-check. X pays 7 × 40 = Rs. 280 and Z pays 11 × 40 = Rs. 440. Adding the three payments, 280 + 320 + 440 = Rs. 1,040, which is exactly the amount the three of them handed over, so the split is internally consistent.