Question

A man divides Rs. 8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew, and each son receives five times as much as each nephew, how much does each daughter receive?

• A. INR 800
• B. INR 600
• C. INR 1600
• D. INR 1800

Hint:

Setting the smallest unit (the nephew's share) as $x$ keeps the algebraic equations simple and avoids the use of fractions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires partitioning a total sum based on the relative ratios of shares among different groups of heirs.
Detailed Explanation:
Let the share of each nephew be $x$ Rs.
Based on the given conditions:
- Each daughter receives: $4x$ Rs.
- Each son receives: $5x$ Rs.
Set up the equation for the total sum of money shared among 5 sons, 4 daughters, and 2 nephews: \[ (5 \times \text{Son's share}) + (4 \times \text{Daughter's share}) + (2 \times \text{Nephew's share}) = 8600 \] \[ (5 \times 5x) + (4 \times 4x) + (2 \times x) = 8600 \] \[ 25x + 16x + 2x = 8600 \] \[ 43x = 8600 \] \[ x = \frac{8600}{43} = 200 \text{ Rs} \] Thus, the share of each nephew is Rs. 200.
Calculate the share of each daughter: \[ \text{Daughter's share} = 4x = 4 \times 200 = 800 \text{ Rs} \] Each daughter receives INR 800.

Step 2: Final Answer:
The amount each daughter receives is INR 800, matching Option (A).