Introduction / Context:
This question involves division of an amount using a ratio that itself is given in fractional form. Ratios with fractions can appear confusing at first, but they can be converted to simple whole number ratios with an appropriate method. The setting of a will dividing wealth between a son and a daughter is common in aptitude questions and tests your ability to handle fractional ratios and large sums together.
Given Data / Assumptions:
- Total wealth to be divided = Rs 11,50,000.
- Ratio of son : daughter = 2/3 : 5/4.
- We need the son’s share, reported in lakhs of rupees.
Concept / Approach:
First, convert the fractional ratio 2/3 : 5/4 into a whole number ratio by eliminating denominators. This is done by multiplying both fractions by the least common multiple of their denominators. Once we obtain an integer ratio, we can treat it as the usual a : b sharing ratio, where the total is divided in proportion to the sum of the parts. Then the son’s share is calculated as son’s parts over total parts, multiplied by the total wealth.
Step-by-Step Solution:
1) Given ratio of son : daughter = 2/3 : 5/4.
2) Denominators are 3 and 4; their LCM is 12.
3) Multiply each term by 12 to clear denominators.
4) Son’s part = (2/3) * 12 = 8.
5) Daughter’s part = (5/4) * 12 = 15.
6) So the equivalent whole number ratio is son : daughter = 8 : 15.
7) Total number of parts = 8 + 15 = 23.
8) Son’s share = (8 / 23) * 11,50,000 rupees.
9) Compute 11,50,000 * 8 = 92,00,000.
10) Divide by 23: 92,00,000 / 23 = 4,00,000 rupees.
11) Convert to lakhs: 4,00,000 rupees = 4 lakhs.
Verification / Alternative check:
We can also calculate the daughter’s share to confirm the total. Daughter’s share = (15 / 23) * 11,50,000 = (15 * 11,50,000) / 23. This equals 11,50,000 - 4,00,000 = 7,50,000 rupees by complementary calculation. Sum of shares = 4,00,000 + 7,50,000 = 11,50,000 rupees, exactly the given total wealth. The ratio of 4,00,000 : 7,50,000 simplifies by dividing by 50,000 to 8 : 15, which matches the converted ratio, confirming that our calculations are correct.
Why Other Options Are Wrong:
Options A (5), B (6) and C (7) lakhs represent larger shares than what correctly arises from the ratio 8 : 15 when applied to Rs 11,50,000. Option E (3.5 lakhs) is smaller than the correct value and would not yield the given ratio when paired with the daughter’s corresponding share. Only 4 lakhs for the son produces the correct fraction of the total wealth and maintains the converted ratio.
Common Pitfalls:
A very common mistake is to mis-handle the fractional ratio and treat 2/3 and 5/4 directly as integers, or to simply add the fractions without converting them into an integer ratio. Another error is miscalculating the LCM of the denominators or incorrectly multiplying the fractions. To avoid these issues, always clear the denominators first and convert all fractional ratios into simple integer parts before distributing the total amount.
Final Answer:
The son’s share of the wealth is
4 lakhs (Rs 4,00,000).
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