Question

st. 17
BE
Q2). The numerator of a rational numbers is a
3 less than its denominator. If the rumerator
is increased by 8 and denominator in increased by 14, we again get the same rational number
Find the rational number​

Answer 1

Answer:

4/7

Step-by-step explanation:

Let, the denominator be = x

Numerator = x - 3

The number is = (x- 3)/x

Again,

Numerator increased by 8 = x - 3 +8 = x + 5

Denominator decreased by 14 = x+14

The number is = (x+5)/(x+14)

Therefore , (x-3) / x = (x+5) / ( x+14)

or, (x-3) (x+14) = x( x+5)

or, x ( x + 14) -3 ( x + 14) = $x^{2}$ + 5x

or, $x^{2}$ + 14x - 3x - 42 = $x^{2}$ + 5x

or, $x^{2}$ - $x^{2}$ + 11x - 5x = 42

or, 6x = 42

or, x = 42/6

or, x = 7

Therefore the denominator is = 7

The numerator is = x - 3 = 7 - 3 = 4

The number is = 4/7