Introduction / Context:
This question is a direct application of the ratio concept used to share a total sum among several people. You are given the ratio of shares of A, B and C and the actual amount received by one person. From this information, you need to reconstruct the total amount. This type of question frequently appears in banking, SSC and other competitive examinations.
Given Data / Assumptions:
- Ratio of A : B : C = 5 : 6 : 9.
- Amount received by A = Rs 450.
- The entire sum is fully distributed among A, B and C according to this ratio.
Concept / Approach:
When amounts are divided in a ratio, each term in the ratio corresponds to a proportional part of the total. If A gets 5 parts, B gets 6 parts and C gets 9 parts, then the total number of parts is 5 + 6 + 9. If we know the amount corresponding to one person’s parts, we can find the value of a single part and then the total sum. The key idea is to treat the ratio numbers as multiples of some common factor k and solve for k using the known share.
Step-by-Step Solution:
1) Let the common multiplying factor be k.
2) Then the share of A = 5k, share of B = 6k and share of C = 9k.
3) According to the question, A receives Rs 450, so 5k = 450.
4) Solve for k: k = 450 / 5 = 90.
5) Total number of parts = 5 + 6 + 9 = 20 parts.
6) Total sum = 20k = 20 * 90 = Rs 1,800.
Verification / Alternative check:
We can calculate the amount for B and C using k = 90 as a check. B gets 6k = 6 * 90 = Rs 540. C gets 9k = 9 * 90 = Rs 810. Now sum these: 450 + 540 + 810 = 1,800. This equals the total sum we obtained, validating that the ratio and the computations are all correct. This balance check is useful in exam conditions to avoid silly mistakes.
Why Other Options Are Wrong:
Option A (Rs 2,000), option C (Rs 2,250), option D (Rs 1,000) and option E (Rs 1,500) do not satisfy the condition that A’s share is exactly 5 parts equal to Rs 450. For example, if the total were Rs 2,000, each part would be Rs 100, so A would get 5 * 100 = Rs 500, which is incorrect. Similar mismatches happen with the other totals. Only Rs 1,800 leads to A receiving Rs 450 when using the ratio 5 : 6 : 9.
Common Pitfalls:
A common mistake is to directly divide A’s share by the total number of ratio terms instead of using only A’s ratio term. Another error is adding the ratio numbers incorrectly or miscomputing the value of k. Carefully setting up the relationship between the known share and the ratio term (5k = 450 here) is essential to get the correct result.
Final Answer:
The total sum of money that was divided among A, B and C is
Rs 1,800.
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