The ratio of ages of A and B is 3 : 5. If the sum of their ages is 32 years, what is A’s age?

Appeared in: AIIMS Delhi NO- 2019

Explanation

The problem is solved by representing the ages as 3x and 5x based on the 3:5 ratio.
An equation is formed from the sum of their ages: 3x + 5x = 32, which simplifies to 8x = 32.
Solving for the common multiplier 'x' gives x = 4.
A's age is then calculated as 3 times the common multiplier (3 * 4), which equals 12 years.

Option A: If A's age were 10, the common multiplier 'x' would be 10/3. This would make the sum of ages 8 * (10/3) = 80/3, which is not 32.
Option C: If A's age were 15, the common multiplier 'x' would be 5 (since 3 * 5 = 15). The sum of ages would then be 8x = 8 * 5 = 40, which contradicts the given sum of 32.
Option D: This value represents the age of B, not A. Using the calculated common multiplier x=4, B's age is 5x = 5 * 4 = 20. The question specifically asks for A's age.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving age-related word problems using ratios and linear equations as background academic context rather than a clinical decision trigger.
This type of ratio problem is a fundamental mathematical skill applicable in many fields, including science and healthcare.
In nursing, understanding ratios is critical for tasks like calculating medication dosages, diluting solutions, and interpreting lab results that are expressed as ratios.
For example, a medication might need to be mixed in a 1:10 ratio with a saline solution. Correctly calculating the required volumes is essential for patient safety.

How to Approach the Question

First, carefully read the problem to identify the key pieces of information: the ratio of the quantities (3:5) and their total sum (32).
Represent the unknown quantities using the ratio and a common variable, 'x'. In this case, the ages are 3x and 5x.
Formulate an algebraic equation that reflects the relationship described in the problem. Here, the sum of the ages is 32, so 3x + 5x = 32.
Solve the equation for 'x'. Combine the 'x' terms (8x = 32) and then isolate 'x' by division (x = 4).
Use the value of 'x' to find the specific quantity asked for in the question. The question asks for A's age, which is 3x, so calculate 3 * 4.
As a final check, calculate the other quantity (B's age) and verify that their sum matches the total given in the problem (12 + 20 = 32).

Concept Tested & Keywords

Concept Tested: Solving age-related word problems using ratios and linear equations.
Stem keywords: ratio of ages, sum of their ages, 3 : 5, 32 years
Lead-in keywords: what is

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Practise the full AIIMS Delhi NO- 2019

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