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    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?
    A 4 yrs Correct Answer Incorrect Answer
    B 6 yrs Correct Answer Incorrect Answer
    C 12 yrs Correct Answer Incorrect Answer
    D 10 yrs Correct Answer Incorrect Answer

    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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