A mother is currently twice as old as her daughter. 20 years ago, the age of the mother was 12 times the age of daughter. The present age of the mother in year is ....................

1. A

   22

2. B

   44

3. C

   32

4. D

   34

Appeared in: ESIC Nursing Officer 2016 (Shift -2)

Explanation

• The problem provides two conditions that can be translated into a system of two linear equations: M = 2D (present condition) and M - 20 = 12(D - 20) (past condition).
• By substituting the first equation into the second, we can solve for the daughter's age (D). The equation becomes 2D - 20 = 12D - 240, which simplifies to 10D = 220, so D = 22 years.
• Using the daughter's age (D=22), the mother's age (M) can be found using the first equation: M = 2 * D, which gives M = 2 * 22 = 44 years.

Why Other Options Were Wrong

• Option A: This is the calculated present age of the daughter, not the mother. The question specifically asks for the mother's present age.
• Option C: If the mother's age is 32, her daughter's age would be 16 (since M=2D). Twenty years ago, the daughter's age would have been 16 - 20 = -4, which is impossible.
• Option D: If the mother's age is 34, her daughter's age would be 17. Twenty years ago, the daughter's age would have been 17 - 20 = -3, which is also impossible.

Related Visual

• Visual 1: No visual is required for this type of question as it is based on mathematical calculation.

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.
• This question tests basic mathematical and logical reasoning skills, which are part of the general aptitude section in many nursing entrance exams.
• The ability to translate word problems into mathematical expressions is a fundamental skill for analyzing data and performing calculations in various settings.
• What if? If the condition was '10 years ago' instead of 20, the equation would be M-10 = 12(D-10). Solving this would yield D=11 and M=22, making the mother's age 22.

How to Approach the Question

• First, carefully read the problem to identify the unknowns and the relationships between them. Assign variables to the unknowns, such as 'M' for the mother's present age and 'D' for the daughter's present age.
• Translate each statement in the word problem into a mathematical equation. The first sentence gives the present relationship (M = 2D), and the second gives the past relationship (M - 20 = 12(D - 20)).
• You now have a system of two linear equations. Use the substitution or elimination method to solve for one of the variables. Substituting '2D' for 'M' in the second equation is the most direct path.
• Solve the resulting single-variable equation to find the value of that variable (in this case, D).
• Substitute the value you just found back into one of the original, simpler equations to find the value of the other variable (M).
• Finally, re-read the question to ensure you are answering what is being asked (the mother's age) and not another value you calculated along the way (the daughter's age).

Concept Tested & Keywords

• Concept Tested: Solving age-related word problems using a system of linear equations.
• Stem keywords: mother, daughter, age, twice, 20 years ago, 12 times
• Lead-in keywords: present age

Question ID

QdUIChXNCJC83_7_XMQzKx

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