The sum of the numerator and denominator of a fraction is 12. If the d

1.	The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.
Answer» Let’s assume the numerator of the fraction to be x and the denominator of the fraction to be y. So, the required fraction is x/y. From the question it’s given as, The sum of the numerator and denominator of the fraction is 12. Thus, the equation so formed is, x + y = 12 ⇒ x + y – 12 = 0 And also it’s given in the question as, If the denominator is increased by 3, the fraction becomes 1/2. Putting this as an equation, we get x/ (y+3) = 1/2 ⇒ 2x = (y+3) ⇒ 2x – y – 3 = 0 The two equations are, x + y – 12 = 0…… (i) 2x – y – 3 = 0…….. (ii) Adding (i) and (ii), we get x + y – 12 + (2x – y – 3) = 0 ⇒ 3x -15 = 0 ⇒ x = 5 Using x = 5 in (i), we find y 5 + y – 12 = 0 ⇒ y = 7 Therefore, the required fraction is \(\frac{5}{7}\).

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.

Answer»

Let’s assume the numerator of the fraction to be x and the denominator of the fraction to be y.

So, the required fraction is x/y.

From the question it’s given as,

The sum of the numerator and denominator of the fraction is 12.

Thus, the equation so formed is,

x + y = 12

⇒ x + y – 12 = 0

And also it’s given in the question as,

If the denominator is increased by 3, the fraction becomes 1/2.

Putting this as an equation, we get

x/ (y+3) = 1/2

⇒ 2x = (y+3)

⇒ 2x – y – 3 = 0

The two equations are,

x + y – 12 = 0…… (i)

2x – y – 3 = 0…….. (ii)

Adding (i) and (ii), we get

x + y – 12 + (2x – y – 3) = 0

⇒ 3x -15 = 0

⇒ x = 5

Using x = 5 in (i), we find y

5 + y – 12 = 0

⇒ y = 7

Therefore, the required fraction is \(\frac{5}{7}\).