At present Reena is twice as old as Sunita. Three years ago, Reena was three times as old as Sunita was. How old is Reena now?

Appeared in: BSF Staff Nurse - 2021

Explanation

Let Reena's current age be R and Sunita's be S. The problem provides two conditions that can be translated into equations.
The first condition, 'Reena is twice as old as Sunita,' gives the equation R = 2S.
The second condition, 'Three years ago, Reena was three times as old as Sunita,' gives the equation R - 3 = 3(S - 3).
By substituting the first equation into the second (2S - 3 = 3S - 9), we can solve for Sunita's age, S, which is 6 years.
Using Sunita's age, we find Reena's age with the first equation: R = 2 * 6 = 12 years.

Option A: This is Sunita's current age, not Reena's. The question specifically asks for Reena's age.
Option B: If Reena is 8, Sunita would be 4 (to be twice as old). Three years ago, their ages would have been 5 and 1. 5 is not three times 1, so this option is incorrect.
Option C: If Reena is 10, Sunita would be 5. Three years ago, their ages would have been 7 and 2. 7 is not three times 2, so this option is incorrect.

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 a system of linear equations as background academic context rather than a clinical decision trigger.
While not a clinical question, aptitude for logical reasoning and mathematical problem-solving is a key component of many nursing entrance and competitive examinations.
This skill is foundational for critical nursing tasks such as calculating medication dosages, titrating IV drips, and interpreting data from patient monitoring charts.
What if the question stated Reena was three times as old as Sunita at present? The equations would change to R=3S and R-3=3(S-3), which would lead to an impossible result (3S-3 = 3S-9), indicating an error in the problem's premise.

How to Approach the Question

First, carefully read the problem to identify the unknowns and the relationships between them. Assign variables, such as 'R' for Reena's age and 'S' for Sunita's age.
Translate the word statements into mathematical equations. 'Reena is twice as old as Sunita' becomes R = 2S.
For conditions set in the past or future, adjust the variables accordingly. 'Three years ago' means using (R - 3) and (S - 3).
Set up the second equation for the past condition: R - 3 = 3(S - 3).
You now have a system of two linear equations. Use substitution (replacing R with 2S in the second equation) to solve for one variable.
After finding the value of one variable (S = 6), substitute it back into the simpler equation (R = 2S) to find the final answer.

Concept Tested & Keywords

Concept Tested: Solving age-related word problems using a system of linear equations.
Stem keywords: Reena, Sunita, age, twice as old, three years ago, three times as old
Lead-in keywords: How old is Reena now

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Practise the full BSF Staff Nurse - 2021

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