Investment split from a total: Amit and Sudesh invest in the ratio 4 : 7. If the sum of their investments is ₹ 49,500, compute Sudesh’s investment by converting the ratio to parts of the whole.
Correct Answer: ₹ 31500
Introduction / Context: Turning a ratio into absolute amounts requires finding the value of one part. Once the sum corresponds to the total parts, multiply by the relevant number of parts to get an individual’s share.
Given Data / Assumptions:
- Amit : Sudesh = 4 : 7.
- Total = ₹ 49,500.
Concept / Approach: Total parts = 4 + 7 = 11. One-part value = 49,500 / 11. Sudesh’s share = 7 parts.
Step-by-Step Solution:
One part = 49,500 / 11 = 4,500.Sudesh’s investment = 7 * 4,500 = ₹ 31,500.Verification / Alternative check: Amit’s share = 4 * 4,500 = ₹ 18,000. Sum 31,500 + 18,000 = 49,500, matching the total and preserving 4 : 7.
Why Other Options Are Wrong: ₹ 18,00 (typo), ₹ 18,500, ₹ 31,000, or ₹ 28,000 do not correspond to 7/11 of the total.
Common Pitfalls: Dividing the total by just one of the ratio numbers or forgetting to multiply by the correct number of parts afterwards.
Final Answer: ₹ 31500