A sum was divided between two friends in the ratio 5:11. If one of them gets 1350 more than the other, what was the whole sum?

Appeared in: NORCET 2 - 2021 (shift-1)

Explanation

The shares of the two friends can be represented as 5x and 11x, based on the given 5:11 ratio.
The problem states the difference between the shares is 1350, which allows us to create the equation: 11x - 5x = 1350.
Solving this equation (6x = 1350) gives the value of the common multiplier, x = 225.
The total sum is the sum of the ratio parts multiplied by x. The total ratio parts are 5 + 11 = 16.
Therefore, the total sum is 16 * 225, which equals 3600.

Option A: This value would result if there was a calculation error, such as incorrectly calculating the value of 'x' as 250 (4000 / 16 = 250). If x were 250, the difference would be 6 * 250 = 1500, not 1350.
Option C: This answer does not align with the ratio and difference provided. 3400 is not divisible by the total ratio parts (16), indicating it cannot be the correct total sum based on the problem's parameters.
Option D: This value might be chosen due to a calculation error. For instance, if one incorrectly assumed the total sum was 15 times the multiplier (instead of 16), 15 * 225 = 3375, which is close to 3300. However, the correct total ratio is 16.

Visual 1: Bar Chart - A chart visually representing the two shares (a bar of 5 units and a bar of 11 units) and highlighting that the difference (6 units) corresponds to the value 1350.

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.
While this is a mathematics question, quantitative reasoning is a critical skill for nurses and is tested in the General Intelligence/Aptitude section of nursing entrance exams.
Nurses frequently use ratios and proportions for tasks like medication dosage calculations, IV drip rate adjustments, and interpreting lab results.
What if? - If the ratio was 5:8 instead of 5:11, the difference in ratio parts would be 3 (8-5). The equation would be 3x = 1350, making x = 450. The total sum would then be (5+8) * 450 = 13 * 450 = 5850.

How to Approach the Question

First, carefully read the problem to identify the key pieces of information: the ratio (5:11) and the difference in value between the parts (1350).
Represent the unknown shares using a variable. Let the shares be 5x and 11x.
Set up an algebraic equation based on the relationship described. Here, the difference is given: 11x - 5x = 1350.
Solve the equation to find the value of 'x'. This value is the common multiplier for the ratio.
Use the value of 'x' to answer the question. The question asks for the 'whole sum', which is the total of the two shares (5x + 11x = 16x).
Calculate the final answer (16 * x) and verify it against the given options.

Concept Tested & Keywords

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Practise the full NORCET 2 - 2021 (shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.