The sum of 3 numbers is 52. The ratio of the first to second is 4:5 and that of second to third is 3:5. Find the second number?

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

The first step is to combine the two ratios (First:Second = 4:5 and Second:Third = 3:5) into a single continuous ratio.
To combine them, the common term (the second number) must be made equal. The LCM of 5 and 3 is 15.
Multiplying the first ratio by 3 and the second by 5 gives the combined ratio of First:Second:Third as 12:15:25.
Let the numbers be 12x, 15x, and 25x. Their sum is 52x.
Given the sum is 52, we have 52x = 52, which means x = 1.
The second number is 15x, so it is 15 * 1 = 15.

Option A: The value 20 is the result of an incorrect calculation. It does not correspond to any of the numbers when the ratios are correctly combined and solved.
Option C: The value 5 is the component for the second number in the first ratio (4:5). This is a common error where a part of the initial, uncombined ratio is mistaken for the final answer.
Option D: The value 10 is an arbitrary number that results from a calculation error. It might be obtained by incorrectly doubling the '5' from the first ratio, but it has no logical basis in the problem's solution.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving problems involving combined ratios and proportions as background academic context rather than a clinical decision trigger.
This question tests foundational mathematical aptitude, a skill necessary for various calculations in professional fields, including dosage calculations in nursing.
Strong quantitative reasoning helps in interpreting data, charts, and other numerical information accurately.
What if the ratio of the second to the third number was 5:3 instead? The combined ratio would become 12:15:9. The sum would be 36x = 52, so x = 52/36 = 13/9. The second number would then be 15 * (13/9) = 65/3 or approximately 21.67.

How to Approach the Question

First, read the question carefully to identify the given information: the sum of three numbers is 52, the ratio of the first to the second is 4:5, and the ratio of the second to the third is 3:5.
Recognize that you have two separate ratios with a common element (the second number). The goal is to create a single, continuous ratio for all three numbers.
Find the Least Common Multiple (LCM) of the parts corresponding to the common element. Here, the parts for the second number are 5 and 3, so the LCM is 15.
Adjust both ratios so the common element's part equals the LCM. This will give you the combined ratio (A:B:C).
Represent the three numbers using a variable 'x' based on the new combined ratio (e.g., Ax, Bx, Cx).
Use the given sum of the numbers to create an equation and solve for 'x'.

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-2)

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