Question

A batch of 36 school children goes for an excursion trip to Nainital. When one 10-year-old child is replaced with another child, the average age of the children in the batch increases by \( 2\frac{1}{2} \) months. What is the age of the new child?

Hint:

Multiply the change in average by the number of members to find the total age difference, then apply it to the replaced individual.

Answer 1

Step 1: Convert the increase in average age to years.
\[ 2\frac{1}{2} \text{ months} = \frac{5}{2} \text{ months} = \frac{5}{24} \text{ years} \] Step 2: Calculate total increase in age for all 36 students. \[ \text{Total increase} = 36 \times \frac{5}{24} = \frac{180}{24} = 7.5 \text{ years} \] Step 3: Since one 10-year-old child is replaced,
The new child must be older than the previous one by 7.5 years: \[ \text{Age of new child} = 10 + 7.5 = \boxed{17.5 \text{ years}} \]