Tina, who is 16 years old, is 4 times as old as her brother. How old will she be when she is twice as old as he?

Appeared in: BHU NO-2019

Explanation

First, determine the brother's current age. Since Tina is 16 and is 4 times as old as her brother, her brother's age is 16 / 4 = 4 years.
Next, set up an equation for the future. Let 'x' be the number of years from now. Tina's future age will be (16 + x), and her brother's will be (4 + x).
The condition is that Tina will be twice as old as her brother, which translates to the equation: 16 + x = 2 * (4 + x).
Solving the equation gives: 16 + x = 8 + 2x, which simplifies to x = 8. This means the event happens in 8 years.
The question asks for Tina's age at that time, which is her current age plus the years passed: 16 + 8 = 24 years.

Option A: This is an incorrect calculation. If Tina is 23, 7 years have passed. Her brother would be 4 + 7 = 11. 23 is not twice 11.
Option B: This is an incorrect calculation. If Tina is 42, 26 years have passed. Her brother would be 4 + 26 = 30. 42 is not twice 30.
Option D: This is an incorrect calculation. If Tina is 32, 16 years have passed. Her brother would be 4 + 16 = 20. 32 is not twice 20.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving age-based word problems using linear equations as background academic context rather than a clinical decision trigger.
This type of logical reasoning is foundational for critical thinking in any field, including interpreting data and patient information in nursing.
It demonstrates the importance of breaking down a problem into smaller, manageable steps: identify knowns, define unknowns, create a model (equation), and solve.
This skill is directly transferable to clinical calculations, such as medication dosages, where setting up and solving proportions and equations is a daily task.

How to Approach the Question

First, carefully read the problem to identify all the given information (the 'knowns'). Here, Tina's age is 16, and she is 4 times her brother's age.
Use the knowns to find any missing initial information. Calculate the brother's current age by dividing Tina's age by 4 (16 / 4 = 4).
Define the future scenario using a variable. Let 'x' be the number of years until the condition is met.
Write an algebraic equation that represents the future relationship: Tina's future age (16 + x) will be twice her brother's future age (4 + x). So, 16 + x = 2 * (4 + x).
Solve the equation for 'x' to find how many years will pass.
Finally, ensure you answer the specific question asked. The question is 'How old will Tina be?', so calculate her future age (16 + x).

Concept Tested & Keywords

Concept Tested: Solving age-based word problems using linear equations.
Stem keywords: age problem, Tina, 16 years old, 4 times as old, brother, twice as old
Lead-in keywords: How old will she be

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Practise the full BHU NO-2019

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