Introduction / Context:
This aptitude question is based on the concept of ratio and proportion, specifically on how a fixed sum of money is divided among three people according to a given ratio. Such problems commonly appear in competitive exams to test understanding of how to convert fractional ratios into whole number ratios and then calculate individual shares from the total amount.
Given Data / Assumptions:
- Total amount to be divided = Rs 18,200.
- The ratio of shares of X, Y and Z is 1/3 : 1/4 : 1/2.
Concept / Approach:
To handle ratios containing fractions, we first convert them into whole number ratios. This is done by taking the LCM of the denominators of the fractions and multiplying each term by this LCM. After obtaining a clean whole number ratio, we treat the sum of the ratio terms as the total number of parts into which the amount is divided. Then each person’s share is calculated as (individual parts / total parts) * total amount.
Step-by-Step Solution:
1) The ratio is given as 1/3 : 1/4 : 1/2 for X : Y : Z.
2) Denominators are 3, 4 and 2. The LCM of 3, 4 and 2 is 12.
3) Multiply each term by 12 to convert into whole numbers: (1/3)*12 = 4, (1/4)*12 = 3, (1/2)*12 = 6.
4) So the equivalent ratio becomes X : Y : Z = 4 : 3 : 6.
5) Total number of parts = 4 + 3 + 6 = 13 parts.
6) Each part is equal to 18,200 / 13 = 1,400 rupees.
7) Share of X = 4 parts = 4 * 1,400 = Rs 5,600.
Verification / Alternative check:
We can also compute the shares of Y and Z to verify that the total adds back to 18,200. Y gets 3 * 1,400 = Rs 4,200. Z gets 6 * 1,400 = Rs 8,400. Adding them together: 5,600 + 4,200 + 8,400 = 18,200, which matches the original total. This confirms that our conversion of the fractional ratio into whole number parts and the subsequent calculations are consistent and correct.
Why Other Options Are Wrong:
Option A (Rs 4,400) and option B (Rs 4,200) are actually closer to the amount that Y receives, not X. Option C (Rs 7,000) is larger than the correct value and does not correspond to any correct part-based calculation. Option E (Rs 6,000) also does not match any exact multiple of 1,400, so it cannot represent a valid share based on the derived ratio 4 : 3 : 6.
Common Pitfalls:
Students often forget to convert fractional ratios into whole numbers first and may try to work directly with fractions, which increases the chance of arithmetic errors. Another frequent mistake is to miscalculate the LCM of denominators, which leads to an incorrect whole number ratio and wrong final answers. Some learners also divide the total amount by an incorrect number of ratio parts or mix up whose share corresponds to which part in the final ratio.
Final Answer:
Therefore, the share of X from the amount of Rs 18,200 is
Rs 5,600.
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