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Rani, who is y years old at present, is x years older than Hamid. Fifteen years ago, Hamid's age was 1/4 of the age of Rani. Which of the following is true ?

Rani, who is y years old at present, is x years older than Hamid. Fifteen years ago, Hamid's age was 1/4 of the age of Rani. Which of the following is true ? Correct Answer 3y - 4x = 45

Given:

The present age of Rani = y

Rani is x year older than Hamid

Fifteen years ago, Hamid's age was 1/4 of the age of Rani

Calculation:

Age of Hamid + x years = age of Rani

Age of Hamid = age of Rani - x = y - x

According to the question:

Fifteen years ago, the age of Hamid = y - x - 15

Fifteen years ago, the age of Rani = y - 15

Hence, y - x - 15 = 1/4 × (y - 15)

⇒ 4y - 4x - 60 = y - 15

⇒ 3y - 4x = 45

Hence option 1 is correct i.e. 3y - 4x = 45

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