Question

Q18: 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 obtained is
3/2. Find the rational number.​

Answer 1

Answer:

Let the numerator of a rational be x

then, denominator = x+8

according to your question

x + 17 = 3

x+8-1 2

x + 17 = 3

x + 7 2

cross multiplication gives

3x + 21 = 2x + 34

3x - 2x = 34 - 21

x = 13

Hence Numerator = x = 13

& Denominator = x + 8 = 13 + 8 = 21

so, the rational number = 13

21

Answer 2

Solution

Given :-

• 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 obtained is 3/2

Find :-

• These Fraction

Explanation

Let,

• Numerator be = x
• Denominator be = y

A/C to question,

(The denominator of a rational number is greater than its numerator by 8. )

==> y = x + 8

==> x - y = -8 ---------(1)

Again,

(If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2 )

==> ( x + 17)/(y -1) = 3/2

==> 2 * (x+17) = 3 * (y-1)

==> 2x - 3y = -3 - 34

==> 2x - 3y = - 37 ----------(2)

Multiply by 2 in equ(1) & 1 in equ(2)

• 2x - 2y = -16
• 2x - 3y = -37

_________________Sub . it's

==> 3y - 2y = -16 + 37

==> y = 21

Keep Value of y in equ(1)

==> x - (21) = -8

==> x = - 8 + 21

==>x = 13

________________________

Hence

• Fraction will be x/y = 13/21

_________________