DVD rent split by usage time: Samiara, Mahira, and Kiara jointly rent DVDs for ₹ 578. They use them for 8 hours, 12 hours, and 14 hours respectively. Assuming rent is shared in proportion to hours of use, what is Kiara’s share?

Introduction / Context:
When a common resource is rented and used unevenly, a common fair-division rule is to split the rent in proportion to each person’s usage time. This question applies that idea to three friends renting DVDs together for a fixed fee.

Given Data / Assumptions:

• Total rent = ₹ 578.
• Usage times: 8 h (Samiara), 12 h (Mahira), 14 h (Kiara).
• Rent is split proportional to usage hours.

Concept / Approach:
Let the shares be proportional to 8 : 12 : 14. Reduce the ratio to its simplest terms to make arithmetic easier, sum the parts, and then allocate the total rent according to each person’s part share. Kiara’s share corresponds to the last term of the ratio after reduction.

Step-by-Step Solution:

Verification / Alternative check:
Samiara = 4 * 34 = 136; Mahira = 6 * 34 = 204; Kiara = 7 * 34 = 238; Sum = 578, consistent.

Why Other Options Are Wrong:
₹ 204 is Mahira’s share, not Kiara’s. ₹ 192 and ₹ 215 do not align with the exact part value 34. ₹ 225 is an arbitrary round figure.

Common Pitfalls:
Forgetting to reduce ratios or miscomputing the per-part value by not dividing the total correctly.

Final Answer:
₹ 238