Question
The average age of 15 students in a classroom is 20 years.
When two new students, Raj and Simran, join the class, their ages being in the ratio of 7:8, the overall average age increases by 3 years. What is the age difference between Raj and Simran?Solution
ATQ,
Total age of 15 students = (20 × 15) = 300 years
Total age of 17 students = (23 × 17) = 391 years
Total age of ‘Raj’ and ‘Simran’ = (391 – 300) = 91 years
Let the ages of ‘Raj’ and ‘Simran’ be ‘7x’ years and ‘8x’ years, respectively.
So, (7x + 8x) = 91
Or, 15x = 91
Or, x = 6.07 (rounded to 6)
Therefore, required difference = (8x – 7x) = x = 6 years
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