From a class of 42 boys, a boy aged 10 years goes away and in his place, a new boy is admitted. If on account of this change, the average age of the boys in that class increases by 2 months, the age of the new comer is :

1. A

   19 years

2. B

   17 years

3. C

   10 yr. 6 month

4. D

   12 yr. 2 month

Appeared in: RRB Staff Nurse Delhi-2015

Explanation

• The core principle is that the total change in the sum of ages is equal to the number of individuals multiplied by the change in their average age.
• First, calculate the total increase in age for the entire class: 42 boys × 2 months = 84 months.
• Convert this total increase into years for easier calculation: 84 months / 12 months per year = 7 years.
• This 7-year increase represents the difference in age between the new boy and the boy who left. Since the average increased, the new boy is older.
• Therefore, the newcomer's age is the age of the boy who left plus the total increase: 10 years + 7 years = 17 years.

Why Other Options Were Wrong

• Option A: If the newcomer were 19 years old, the net increase in the total age of the class would be 9 years (19 - 10). This would raise the average age by (9 years * 12 months/year) / 42 boys ≈ 2.57 months, which is more than the stated 2 months.
• Option C: An age of 10 years and 6 months is only 6 months older than the boy who left. This small difference would only increase the average age by 6 months / 42 boys ≈ 0.14 months, which is far less than the required 2 months.
• Option D: An age of 12 years and 2 months represents an increase of 2 years and 2 months (26 months) over the boy who left. This would increase the average age by 26 months / 42 boys ≈ 0.62 months, which is not the stated 2 months.

Related Visual

• Visual 1: Flowchart - A flowchart illustrating the calculation steps: (1) Multiply number of boys by average increase (42 x 2 = 84 months). (2) Convert total increase to years (84 / 12 = 7 years). (3) Add increase to the age of the boy who left (10 + 7 = 17 years).

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Average and Age Problems as background academic context rather than a clinical decision trigger.
• This is a general aptitude question testing mathematical reasoning, not a clinical nursing concept.
• Skills in calculating averages are fundamental in many fields, including data analysis and research, but this specific problem does not have a direct nursing application.
• What if the average age had decreased by 2 months? In that case, the newcomer would be younger. The total decrease would be 7 years, and the newcomer's age would be 10 - 7 = 3 years old.

How to Approach the Question

• First, identify the key information provided: the total number of individuals (42 boys), the age of the person leaving (10 years), and the change in the average age (+2 months).
• The most efficient method is to calculate the total change in the sum of ages. This is found by multiplying the number of individuals by the change in the average.
• Calculate the total increase: 42 boys × 2 months = 84 months.
• Convert units to be consistent. Since the initial age is in years, convert the total increase to years: 84 months ÷ 12 = 7 years.
• Understand that this total increase is the difference between the newcomer's age and the age of the person who left.
• Since the average increased, the newcomer must be older. Add the total increase to the age of the person who left: 10 years + 7 years = 17 years.

Concept Tested & Keywords

• Concept Tested: Average and Age Problems
• Stem keywords: class of 42 boys, aged 10 years, new boy is admitted, average age increases by 2 months
• Lead-in keywords: the age of the new comer is

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