The ratio of the ages of A and B is 3:4. After 10 years, the ratio becomes 4:5. Find the present age of A.

Appeared in: DSSSB 6 September 2024

Explanation

The present ages of A and B can be represented as 3x and 4x, based on the initial 3:4 ratio.
After 10 years, their ages become (3x + 10) and (4x + 10), and the new ratio is given as 4:5.
An equation is formed: (3x + 10) / (4x + 10) = 4/5.
Solving this equation for the common multiplier 'x' yields x = 10.
A's present age is 3x, which is calculated as 3 * 10 = 30 years.

Option A: If A's present age is 20, then 3x = 20, making x = 20/3. After 10 years, the ratio of ages would be (20 + 10) / ((4 * 20/3) + 10) = 30 / (110/3) = 9/11, which is not the required 4/5.
Option B: If A's present age is 25, then 3x = 25, making x = 25/3. After 10 years, the ratio of ages would be (25 + 10) / ((4 * 25/3) + 10) = 35 / (130/3) = 21/26, which is not the required 4/5.
Option D: If A's present age is 35, then 3x = 35, making x = 35/3. After 10 years, the ratio of ages would be (35 + 10) / ((4 * 35/3) + 10) = 45 / (170/3) = 27/34, which is not the required 4/5.

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 logical reasoning and mathematical problem-solving is a foundational skill tested in competitive exams to assess analytical abilities.
While not a direct clinical calculation, the ability to set up and solve equations is crucial for tasks like drug dosage calculations, where precision is vital for patient safety.
What if the initial ratio was 2:3 and after 5 years it became 3:4? The same method applies: (2x+5)/(3x+5) = 3/4. This leads to 8x+20 = 9x+15, so x=5. The initial age of A would be 2x = 10 years.

How to Approach the Question

First, identify the key information: the initial ratio of ages (3:4) and the future ratio after a specific time (4:5 after 10 years).
Represent the unknown present ages using a common variable 'x' based on the initial ratio (A's age = 3x, B's age = 4x).
Formulate an equation by incorporating the change over time. The ages after 10 years will be (3x + 10) and (4x + 10).
Set up the proportion based on the future ratio: (3x + 10) / (4x + 10) = 4/5.
Solve the resulting linear equation for 'x' by cross-multiplying.
Finally, substitute the value of 'x' back into the expression for A's present age (3x) to find the answer.

Concept Tested & Keywords

Concept Tested: Solving age-related word problems using ratios and linear equations.
Stem keywords: ratio, ages, A and B, after 10 years
Lead-in keywords: Find the present age

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Practise the full DSSSB 6 September 2024

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