The age of father 10 year ago was thrice the age of his son. Ten year later, father's age will be twice compare to his son. The present ratio of both ages is?

1. A

   5:2

2. B

   7:3

3. C

   9:2

4. D

   13:4

Appeared in: HSSC Staff Nurse - 2015

Explanation

• The problem requires setting up two linear equations based on two conditions: the relationship between the ages 10 years ago and 10 years in the future.
• Let the father's present age be F and the son's be S. The first condition gives the equation F - 10 = 3(S - 10).
• The second condition gives the equation F + 10 = 2(S + 10).
• Solving these two simultaneous equations yields the son's present age (S) as 30 and the father's present age (F) as 70.
• The ratio of their present ages is F : S, which is 70 : 30.
• Simplifying the ratio 70:30 by dividing both sides by 10 gives the final answer, 7:3.

Why Other Options Were Wrong

• Option A: A ratio of 5:2 would mean their ages are, for example, 50 and 20. Ten years ago, they would have been 40 and 10. The father's age (40) would have been four times the son's age (10), not three times as stated in the problem.
• Option C: A ratio of 9:2 would imply ages like 90 and 20. This is an unlikely age combination and does not satisfy the conditions. Ten years ago, they would have been 80 and 10, making the father's age eight times the son's, which is incorrect.
• Option D: A ratio of 13:4 corresponds to ages like 65 and 20. Ten years ago, they would have been 55 and 10. The ratio 55:10 is 5.5:1, not 3:1. This is a result of incorrect calculation.

Related Visual

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 simultaneous linear equations as background academic context rather than a clinical decision trigger.
• This question tests logical reasoning and basic mathematical skills, which are essential for problem-solving in any field.
• While not directly clinical, the ability to perform calculations and follow a logical process is crucial for tasks like medication dosage calculation, interpreting lab results, and managing patient data.
• What if the question asked for the ratio 5 years from now? After finding the present ages (70 and 30), their ages in 5 years would be 75 and 35. The ratio would be 75:35, which simplifies to 15:7.

How to Approach the Question

• First, carefully read the problem to identify the unknowns. Here, the unknowns are the present ages of the father and the son.
• Assign variables to these unknowns, such as 'F' for the father's present age and 'S' for the son's present age.
• Translate each condition given in the word problem into a mathematical equation. '10 years ago' means you subtract 10 from the present ages (F-10, S-10). '10 years later' means you add 10 (F+10, S+10).
• You will get a system of two linear equations with two variables. Solve these equations simultaneously. A common method is substitution, where you solve one equation for one variable (e.g., F = 3S - 20) and substitute that expression into the other equation.
• Once you find the value of one variable (e.g., S = 30), substitute it back into one of the original equations to find the other variable (F = 70).
• Finally, calculate the required ratio using the present ages (70:30) and simplify it to its lowest terms (7:3) before selecting the correct option.

Concept Tested & Keywords

• Concept Tested: Solving age-related word problems using simultaneous linear equations.
• Stem keywords: age, father, son, ratio, 10 year ago, ten year later
• Lead-in keywords: present ratio

Question ID

Qa5oF9jywDEVETLs_ws-ze

Copy ID