A sum was divided between two friends in the ratio 5:11. If one of them gets Rs.1,350 more than the other, what are the whole sum?

Appeared in: BSF Staff Nurse - 2015

Explanation

The core of the problem is to find the value of one 'part' of the ratio.
The difference in the ratio (11 - 5 = 6 parts) corresponds to the monetary difference (Rs. 1,350).
By dividing Rs. 1,350 by 6, we find that one part is equal to Rs. 225.
The total sum is represented by the total number of parts (5 + 11 = 16).
Multiplying the total parts by the value of one part (16 × 225) gives the total sum of Rs. 3,600.

Option A: Rs. 3,300 is incorrect. This value might be obtained by miscalculating the value of one part or the total number of parts.
Option B: Rs. 3,400 is an incorrect calculation. It does not correspond to the product of the total ratio parts (16) and the value of one part (Rs. 225).
Option D: Rs. 4,000 is incorrect. This might result from an arithmetic error, such as incorrectly calculating 16 x 225.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving word problems involving ratios and proportions as background academic context rather than a clinical decision trigger.
This question tests general aptitude and quantitative reasoning, which are essential skills for nurses.
Nurses often need to perform calculations for medication dosages, IV drip rates, and patient intake/output, all of which require strong mathematical and problem-solving abilities.
What if the ratio was 2:7 and the difference was Rs. 1,000? The difference in parts would be 7 - 2 = 5. One part would be 1000 / 5 = Rs. 200. The total sum would be (2+7) * 200 = 9 * 200 = Rs. 1,800.

How to Approach the Question

First, read the problem carefully to identify the key information: the ratio (5:11) and the difference in value (Rs. 1,350).
Determine the difference in terms of 'parts' of the ratio: 11 parts - 5 parts = 6 parts.
Equate this difference in parts to the monetary difference given in the problem: 6 parts = Rs. 1,350.
Calculate the value of a single 'part' by dividing the monetary value by the number of parts: Rs. 1,350 / 6 = Rs. 225 per part.
Find the total number of parts in the sum: 5 parts + 11 parts = 16 parts.
Calculate the total sum by multiplying the total number of parts by the value of one part: 16 parts × Rs. 225/part = Rs. 3,600.

Concept Tested & Keywords

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