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 BHOPAL NO- 2018( Shift-2nd)

Explanation

The ratio 3:5 implies that the ages can be represented as 3x and 5x, where 'x' is a common multiplier.
The sum of their ages is given as 32, leading to the equation: 3x + 5x = 32.
Solving the equation, 8x = 32, yields the common multiplier x = 4.
A's age is calculated by substituting x into its corresponding ratio part: 3 * 4 = 12 years.

Option A: If A's age were 10, which corresponds to 3x, then x would be 10/3. B's age would be 5 * (10/3) = 50/3. The sum would be 10 + 50/3 = 80/3, which is not 32.
Option C: If A's age were 15, which corresponds to 3x, then x would be 5. B's age would be 5 * 5 = 25. The sum of their ages would be 15 + 25 = 40, not 32.
Option D: This is the age of B, not A. Using the calculated common multiplier x=4, B's age is 5 * 4 = 20 years. This error occurs from solving for the wrong person.

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.
While this is a general aptitude question, the underlying skill of ratio and proportion is critical in nursing.
Nurses frequently use ratio calculations for medication dosages (e.g., mg/kg, mcg/kg/min), titrating IV drips, and diluting solutions.
A strong grasp of these mathematical concepts ensures patient safety by preventing medication errors.

How to Approach the Question

First, identify the key pieces of information: the ratio of ages (3:5) and the total sum of the ages (32).
Represent the unknown ages using a single variable. Let A's age be 3x and B's age be 5x, where 'x' is the common factor you need to find.
Create a linear equation based on the sum: 3x + 5x = 32.
Solve the equation for 'x'. Combine the terms (8x = 32) and then isolate 'x' (x = 32/8).
Once you find 'x', substitute it back into the expression for the age you need to find. The question asks for A's age, which is 3x.
Always double-check if you are solving for the correct person (A or B). A common mistake is to solve for 'x' and stop, or to calculate the age of the wrong person.

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 A’s age
Negative lead-in flag: false

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