Question

In a given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator, it becomes `1/2`. If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes `1/3`. The fraction is ______.

Options

• `13/24`

• `15/26`

• `16/27`

• `16/21`

Answer 1

In a given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator, it becomes `1/2`. If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes `1/3`. The fraction is `underlinebb(15/26)`.

Explanation:

Let the fraction be `x/y`.

From the first condition:

`(x - 1)/(y + 2) = 1/2` 

⇒ 2(x – 1) = y + 2

⇒ y = 2x – 4 

From the second condition:

`(x - 7)/(y - 2) = 1/3` 

⇒ 3(x – 7) = y – 2

⇒ y = 3x – 19

Equate the two expressions for y:

2x – 4 = 3x – 19

⇒ x = 15

Then y = 2(15) – 4

= 26

So, the fraction is `15/26`.