Question

Q.12 The numerator of a rational number is 3 less than its denominator . If numerator is increased by 1 and denominator is increased by 3 then the number becomes 1 /2 Find the rational number.​

Answer 1

Supposition:-

let the denominator be X.

let the numerator be x-3

according to the quest. :-

$\implies$ $\sf\dfrac{x-3+1}{X+3}$ = $\sf\dfrac{1}{2}$

$\implies$ $\sf\dfrac{x-2}{X+3}$ = $\sf\dfrac{1}{2}$

$\implies$ $\sf{\: 2(x-2)}$ = $\sf{\: X+3}$

$\implies$ $\sf{\: 2x-4}$ = $\sf{\: X+3}$

$\implies$ $\sf{\: x}$ = $\sf{\: 7}$

so, the denominator is 7.

and the numerator is 7-3 = 4

hence, the rational no. is $\sf\dfrac{4}{7}$