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: RRB Staff Nurse Kolkata-2015

Explanation

The problem provides two conditions that can be translated into a system of two linear equations. Let R be Reena's age and S be Sunita's age.
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).
Substituting the first equation into the second gives 2S - 3 = 3(S - 3), which simplifies to 2S - 3 = 3S - 9.
Solving for S, we find that Sunita's current age is S = 6 years.
Using R = 2S, Reena's current age is 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: This value does not satisfy the conditions. If Reena is 8, Sunita is 4. Three years ago, they were 5 and 1. 5 is not three times 1.
Option C: This value does not satisfy the conditions. If Reena is 10, Sunita is 5. Three years ago, they were 7 and 2. 7 is not three times 2.

Visual 1: Flowchart - A flowchart illustrating the step-by-step process: 1. Define variables (R, S). 2. Formulate equations from the text. 3. Solve for one variable (S) using substitution. 4. Substitute back to find the other variable (R). 5. Verify the solution.

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 simultaneous linear equations as background academic context rather than a clinical decision trigger.
While not a clinical question, the logical reasoning and problem-solving skills tested are crucial for nurses to interpret patient data, prioritize care, and make sound clinical judgments.
Attention to detail, as demonstrated in correctly translating word problems into equations, is a vital skill for ensuring accuracy in medication dosage calculations and patient assessments.
What if? If the question stated 'In three years, Reena will be twice as old as Sunita', the second equation would change to R+3 = 2(S+3), leading to a different solution.

How to Approach the Question

Step 1: Identify the unknown quantities and assign variables to them (e.g., R for Reena's age, S for Sunita's age).
Step 2: Carefully read the problem statement and translate each piece of information into a mathematical equation.
Step 3: Recognize that you have a system of two equations with two variables. Choose a method to solve it, such as substitution or elimination.
Step 4: Solve for one variable first. In this case, solving for S is straightforward after substitution.
Step 5: Substitute the value you found back into one of the original equations to find the value of the second variable.
Step 6: Reread the question to ensure you are answering what is being asked (Reena's age, not Sunita's) and verify your answer by checking it against the problem's conditions.

Concept Tested & Keywords

Concept Tested: Solving age-based word problems using simultaneous linear equations.
Stem keywords: Reena, Sunita, age, twice as old, three years ago, three times as old
Lead-in keywords: How old

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Practise the full RRB Staff Nurse Kolkata-2015

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