A fraction becomes 5/7, when 2 is subtracted from both the numerator and the denominator. The same fraction becomes 3/4, when 2 are added to both the numerator and the denominator. The difference between numerator and denominator of the fraction is

A fraction becomes 5/7, when 2 is subtracted from both the numerator and the denominator. The same fraction becomes 3/4, when 2 are added to both the numerator and the denominator. The difference between numerator and denominator of the fraction is Correct Answer 8

Let the original fraction be x/y

According to the question, a fraction becomes 5/7, when 2 is subtracted from both the numerator and the denominator

Then,

(x - 2)/(y - 2)= 5/7

⇒ 7x – 14 = 5y – 10

⇒ 7x –5y = 4      ----(i)

The same fraction becomes 3/4, when 2 is added to both the numerator and the denominator

And (x+ 2)/(y+ 2)= 3/4

⇒ 4x + 8 = 3y + 6

⇒ 4x –3y = -2      ----(ii)

Now we multiply equation (i) by 3 and equation (ii) by 5 and subtracting equation (ii) from equation (i), we get

⇒ (21x – 15) – (20x – 15y) = 12 – (-10)

⇒ 21x – 20x = 22

⇒ x = 22

On putting the value of x in equation (i), we get

⇒ 7 × 22 –5y = 4

⇒ 154 –5y = 4

⇒ 5y = 150

⇒ 30

Now to find the difference between numerator and denominator of the fraction

= y – x