According to a will, wealth of Rs 21,25,000 is to be divided between a son and a daughter in the ratio 7/6 : 5/3. How much (in Rs) does the son receive?

Introduction / Context:
This question involves dividing a total amount of wealth between two people using a ratio expressed in fractional form. The ratio between the son and daughter is given as 7/6 : 5/3. We must first simplify this ratio into simple whole-number terms and then apply it to the total wealth. This tests understanding of ratios with fractions and basic percentage-like distribution.

Given Data / Assumptions:
• Total wealth = Rs 21,25,000. • Ratio of son's share to daughter's share = (7/6) : (5/3). • We need to find the son's share in rupees.

Concept / Approach:
When a ratio is given in fractional form, it is often easier to clear the denominators by multiplying each term by the least common multiple of the denominators. This converts the ratio into whole-number terms. Then we treat the ratio as usual: divide the total amount into a number of equal parts equal to the sum of the ratio terms, and multiply the number of parts belonging to each person by the value of one part. This approach avoids dealing with complex fractional amounts directly.

Step-by-Step Solution:
Step 1: The given ratio is (7/6) : (5/3). Step 2: Find the least common multiple of 6 and 3, which is 6. Step 3: Multiply both terms of the ratio by 6 to clear denominators: (7/6) * 6 = 7 and (5/3) * 6 = 10. Step 4: So the simplified ratio of son : daughter is 7 : 10. Step 5: Total parts = 7 + 10 = 17. Step 6: Each part is worth = Total wealth / 17 = 21,25,000 / 17. Step 7: Compute the son's share = 7 parts = 7 * (21,25,000 / 17). Step 8: First calculate 21,25,000 / 17 = 1,25,000. Step 9: Now multiply by 7: 7 * 1,25,000 = 8,75,000.

Verification / Alternative Check:
Check that the daughter's share plus the son's share equals the total. Daughter's share = 10 parts = 10 * 1,25,000 = 12,50,000. Sum of shares = 8,75,000 + 12,50,000 = 21,25,000, which matches the total wealth given. The ratio 8,75,000 : 12,50,000 can be simplified by dividing both amounts by 1,25,000, giving 7 : 10, which matches our simplified ratio. Therefore the son's share is correct.

Why Other Options Are Wrong:
• 12,50,000 corresponds to the daughter's share, not the son's share. • 10,00,000 and 11,25,000 do not maintain the 7 : 10 ratio when paired with the corresponding remaining amounts from the total.

Common Pitfalls:
Some students forget to clear denominators properly, leading to incorrect whole-number ratios. Others mistakenly treat 7/6 and 5/3 as if they are already in a comparable whole-number ratio without adjustment. Always convert fractional ratios to whole-number terms before applying them to totals. Double checking that the shares sum to the total amount and that they maintain the intended ratio is a good final consistency check.

Final Answer:
The son receives Rs 8,75,000 from the total wealth of Rs 21,25,000.