Question

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 ?
1. 3y - 4x = 45
2. 2y - x = 15
3. \(\frac{y}{x} - 15 = \frac{1}{4}\)
4. 3x - 4y = 45

Answer 1

Correct Answer - Option 1 : 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