Question

The numerator of a fraction is 5 less than its denominator. If the numerator is

decreased by 1 and the denominator is increased by 2, then the denominator

becomes three times the numerator. Find the fraction​

Answer 1

Answer:

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.

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