Question

7. The denominator of a rational number is greater than its numerator by 8. If the
numerator is increased by 17 and the denominator is decreased by 1, the number
3
obtained is
Find the rational number.
2​

Answer 1

$\bf{\underline{Question:-}}$

The denominator of a rational number is greater than its numerator by 8. If the

numerator is increased by 17 and the denominator is decreased by 1, the number 3 obtained is Find the rational number.

$\bf{\underline{Solution:-}}$

Let ,

• the numerator of the rational number be x.

So

• as per the given condition, the denominator will be x + 8.

The rational number will be x/x + 8.

According to the given condition,

→ x + 17/x + 8 – 1 = 3/2

→ x + 17/x + 7 = 3/2

→ 2(x + 17) = 3(x + 7)

→ 2x + 34 = 3x + 21

→ 34 − 21 = 3x − 2x

→ x=13

$\bf{\underline{Hence:-}}$

• Numerator of the rational number = x = 13

• Denominator of the rational number = x + 8 = 13 + 8 = 21

• Rational number = 13/21

Answer 2

Answer:

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be xx+8

According to the given condition,

x+17x+8−1=32

 

x+17x+7=32

 

3(x + 7) = 2(x + 17)

3x + 21 = 2x + 34

3x – 2x + 21 – 34 = 0

x – 13 = 0

x = 13

The rational number will be

= xx+8

= 1313+8

Rational number = 13/21