Question

if 1 be reduced from the denominator of a rational number,the value of it becomes 2/3 and if 5 be added to the denominator of the number, the value of the rational number becomes 1/2.Find the number

Answer 1

Let that rational number be a/b where a is numerator and b is denominator
$\frac{a }{b - 1 } = \frac{2}{3}$
3a= 2(b-1). equation number 1
3a= 2b-2
a=
$\frac{2b - 2}{3}$
Now, by second condition
$\frac{a}{b + 5} = \frac{1}{2}$
2a= b+5
a=
$\frac{b + 5}{2}$
now by first and second condition:
$\frac{2b - 2}{3} = \frac{b + 5}{2}$
4b-4= 3b+15
4b-3b= 15+4
b= 19
a=
$\frac{b + 5}{2} = \frac{19 + 5}{2 } = \frac{24}{2} = 12$
a=12, b=19