Question

8.
The denominator of a rational number is greater than its numerator by 7. If 3
is subtracted from the numerator and 2 is added to its denominator, the new
number becomes 1fifth. Find the rational number.
​

Answer 1

Answer:

let the numerator=x

then, " denominator=x+7

a/q

x-3/x+7+2=1/5

x-3/x+9=1/5

5(x-3)=1(x+9)

5x-15=x+9

5x-x=9+15

4x=24

x=24/4

x=6

numerator=x=6

denominator=x+7=6+7=13

the rational no.=6/13

Answer 2

Let numerator be "M".

The denomination of a rational number is greater than it's numerator by 7.

Denomination = M + 7

So,

$\implies$ Fraction = $\dfrac{M}{M\:+\:7}$

If 3 is subtracted from the numerator and 2 is added to the denominator then, the new number becomes 1/5.

According to question,

$\implies\:\dfrac{M\:-\:3}{M\:+\:7\:+\:2}\:=\:\dfrac{1}{5}$

$\implies\:\dfrac{M\:-\:3}{M\:+\:9}\:=\:\dfrac{1}{5}$

Cross multiply them

$\Rightarrow\:5(M\:-\:3)\:=\:1(M\:+\:9)$

$\Rightarrow\:5M\:-\:15\:=\:M\:+\:9$

$\Rightarrow\:5M\:-\:M\:=\:9\:+\:15$

$\Rightarrow\:4M\:=\:24$

$\Rightarrow\:M\:=\:6$

So,

Numerator : M

$\Rightarrow\:6$

Denomination : M + 7

$\Rightarrow\:6\:+\:7$

$\Rightarrow\:13$

Fraction = $\bold{\dfrac{6}{13}}$

∴ Rational number is 6/13.