Samaira, Mahira and Kiara rented a set of DVDs at a rent of ₹ 578. If they used it for 8 hours, 12 hours and 14 hours respectively, what is Kiara's share of rent to be paid?

### Concept & Proportional Rent When a resource is rented jointly, the total rent should be divided among the individuals in the exact ratio of the time each person used the resource. $$ \text{Individual Rent} = \text{Total Rent} \times \left( \frac{\text{Individual Time}}{\text{Total Time}} \right) $$ ### Step-by-Step Solution * **Given:** * Total Rent = ₹ $578$ * Usage time: Samaira = $8$ hours, Mahira = $12$ hours, Kiara = $14$ hours * **Calculation/Deduction:** 1. Determine the ratio of time they used the DVDs: $$\text{Ratio} = 8 : 12 : 14$$ 2. Simplify the ratio by dividing by $2$: $$\text{Ratio} = 4 : 6 : 7$$ 3. Calculate the total number of ratio parts: $$\text{Total Parts} = 4 + 6 + 7 = 17$$ 4. Calculate Kiara's share of the rent (she corresponds to $7$ parts): $$\text{Kiara's Share} = 578 \times \left(\frac{7}{17}\right)$$ 5. Perform the division: $$\frac{578}{17} = 34$$ 6. Multiply by Kiara's ratio: $$\text{Kiara's Share} = 34 \times 7 = 238$$ ### Exam Strategy & Shortcut To quickly divide $578$ by $17$, look at the unit digit. $7 \times 4 = 28$, so the multiplier likely ends in $4$. $17 \times 30 = 510$, leaving $68$, which is $17 \times 4$. So $17 \times 34 = 578$. Then multiply $34 \times 7 = 238$. ### Common Pitfall Forgetting to simplify the initial ratio ($8 : 12 : 14$) can lead to working with unnecessarily large numbers (e.g., dividing by $34$ instead of $17$), which increases calculation time and potential for errors. ### Final Answer Therefore, the correct answer is **₹ 238**.