Question

The numerator of a fraction is 5 less than its
denominator. If 1 is added to the numerator
and to the denominator, the new fraction is 2/3
Find the fraction.​

Answer 1

Given:-

• The numerator of a fraction is 5 less than its denominator.
• If 3 is added to the numerator and denominator both , the fraction becomes 4/5.

To Find:-

• The Original Number.

Solution:-

Let denominator of the fraction be = x

And then numerator be x – 5

Original fraction = (x – 5)/x

According to the Question,

⇒  (x – 5 + 3)/(x + 3) = 4/5

⇒ (x – 2)/(x + 3) = 4/5

⇒ 5(x – 2) = 4x + 12

(By cross multiplication)

⇒ 5x – 10 = 4x + 12

⇒ 5x - 4x = 12 + 10

⇒ x = 22

Original fraction = (x – 5)/x

Original fraction  = (22 – 5)/22

•°•Original fraction = 17/22

Hence, the original number is 17/22.

-----------------------------------------------------------------------------

Hope it helps u : )