A, B and C hire a car for a total charge of Rs. 520 and use it for 7, 8 and 11 hours respectively. If the hire charges are to be shared in proportion to the hours of usage, how much should B pay?

Introduction / Context:
This is a proportional sharing question related to hire charges. Three people A, B and C jointly hire a car and use it for different durations. The total hire charge must be divided among them in proportion to the number of hours each person uses the car. We must calculate the amount B should pay out of the total charge of Rs. 520.

Given Data / Assumptions:

• A uses the car for 7 hours.
• B uses the car for 8 hours.
• C uses the car for 11 hours.
• Total hire charge for the car is Rs. 520.
• Charges are shared in proportion to the hours of usage.
• Each person's share = total charge * (individual hours / total hours).

Concept / Approach:
The underlying concept is direct proportion. Since the same car is used and the charge rate per hour is assumed constant, the cost borne by each person should be directly proportional to the time that person used the car. We first find the total hours of usage and then apply the proportional formula to find B's share of the cost.

Step-by-Step Solution:
Step 1: Add up the total hours of use: Total hours = 7 + 8 + 11 = 26 hours. Step 2: B uses the car for 8 hours. Step 3: B's fraction of the total usage = 8 / 26. Step 4: B's share of the hire charge = total charge * usage fraction = 520 * (8 / 26). Step 5: Simplify the fraction: First, 520 / 26 = 20. Step 6: Then B's share = 20 * 8 = Rs. 160. Step 7: So B should pay Rs. 160 as his part of the hire charges.

Verification / Alternative check:
We can compute the individual shares of A and C to verify. A's share = 520 * (7 / 26) = 20 * 7 = Rs. 140. C's share = 520 * (11 / 26) = 20 * 11 = Rs. 220. Adding all shares gives 140 + 160 + 220 = 520, which matches the total hire charge. This confirms that the proportional allocation is correct.

Why Other Options Are Wrong:
If B paid Rs. 150, Rs. 170 or Rs. 180, his share would no longer be exactly proportional to his 8 hours of usage. The implied rate per hour would be inconsistent with the rates for A and C. Only Rs. 160 maintains the same per hour rate for all three users and ensures that the sum of individual contributions equals the total charge.

Common Pitfalls:
A common mistake is to divide the total charge equally among all three people without considering different usage times. Another mistake is miscalculating the total hours or simplifying the fraction incorrectly. Always add all the hours first, find each person's fraction and then multiply that fraction by the total cost.

Final Answer:
The hire charges paid by B should be Rs. 160.