The sum of 3 numbers is 236. The ratio of the first to second is 3:4 and that of second to third is 5:6. Find the second number?

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

Explanation

The core task is to merge two separate ratios (First:Second and Second:Third) into a single continuous ratio (First:Second:Third).
The common term is the second number, with values 4 and 5. The LCM is 20. Scaling the ratios gives a combined ratio of 15:20:24.
The sum of the ratio parts is 15 + 20 + 24 = 59. The total sum of the numbers is 236. Therefore, one 'part' of the ratio is worth 236 / 59 = 4.
The second number corresponds to 20 parts in the ratio. Its value is calculated as 20 parts × 4 = 80.

Option A: This is the value of the first number, not the second. It is calculated from the first part of the combined ratio (15 parts × 4 = 60).
Option C: This is the value of the third number, not the second. It is calculated from the third part of the combined ratio (24 parts × 4 = 96).
Option D: This value does not align with any of the numbers in the calculated ratio. It likely results from a calculation error, such as incorrectly combining the ratios or an arithmetic mistake when solving for the value of one part.

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 type of ratio problem is a fundamental concept in quantitative aptitude, a section frequently included in competitive exams for various professions, including nursing.
Mastering ratio and proportion is essential for tasks such as medication dosage calculations, where understanding the relationship between drug mass and volume is critical for patient safety.
What if the sum was 472? The value of one part would be 472 / 59 = 8. The second number would then be 20 × 8 = 160.

How to Approach the Question

First, read the question carefully to identify the given information: the total sum (236) and the two separate ratios (3:4 and 5:6).
Recognize that the 'second number' is the common element linking the two ratios.
To create a single continuous ratio, find the Least Common Multiple (LCM) of the values representing the second number in both ratios (4 and 5), which is 20.
Scale both ratios to make the common term equal to the LCM. This will give you the combined ratio for all three numbers.
Sum the parts of the new ratio. Divide the total sum of the numbers (236) by this sum of parts to find the value of a single 'part'.
Finally, multiply the value of a single part by the ratio part that corresponds to the second number to get the final answer.

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.