Question

the dinominator of a rational is greater than its numerator by8.if the numerator is increased by17 and the dinominator is incresad by 1 the no.obtained is3/2.find the rational number​

Answer 1

Given :

• The dinominator of a rational is greater than its numerator by 8.
• if the numerator is increased by 17 and the dinominator is incresad by 1 the no.obtained is 3/2.

To Find :

• Required Fraction = ?

Solution :

Let Numerator be m and Denominator be n.

Therefore, the required fraction will be m/n.

It is given that, the dinominator of a rational is greater than its numerator by 8.

Mathematically it can be expressed as :

→ n = m + 8 ......[Equation (i)]

According to Question now :

→ (m + 17)/n - 1 = 3/2

Cross multiplying both the sides :

→ 2(m + 17) = 3(n - 1)

→ 2m + 34 = 3n - 3

→ 34 + 3 = 3n - 2m

Substituting the value of n from equation (i) we get :

→ 37 = 3(m + 8) - 2m

→ 37 = 3m + 24 - 2m

→ 37 - 24 = 3m - 2m

→ 13 = m

→ m = 13

Now, subsitute the value of m = 13 in equation (i) :

→ n = m + 8

→ n = 13 + 8

→ n = 21

Hence,

• Numerator = m = 13
• Denomintaor = n = 21
• Required Fraction = m/n = 13/21

Answer 2

$\large{\boxed{\boxed{\sf{QUESTION}}}}$

the dinominator of a rational is greater than its numerator by 8.if the numerator is increased by 17 and the dinominator is incresad by 1 the no.obtained is 3/2.find the rational number

$\large{\boxed{\boxed{\sf{ANSWER}}}}$

Rational number = 13/21

____________________

Rational Number

a → Numerator

b → Denominator

We Know That -

$\sf number = \dfrac{numerator}{denominator}$

____________________

$\large{\boxed{\boxed{\sf{LET}}}}$

• the numerator of the rational number be x.

• So according to the given condition, the denominator will be x + 8.

So Now , The rational number will be $\sf \dfrac{x}{x + 8}$

$\large{\boxed{\boxed{\sf{ACCORDING \: TO \: THE \: CONDITION}}}}$

We need to find the value of rational no.

• if the numerator is increased by 17

• the dinominator is incresad by 1

• The no.obtained is 3/2

$\large{\boxed{\boxed{\sf{SOLUTION}}}}$

So , we will write it as

$\sf \Longrightarrow \dfrac{3}{2} = \dfrac{x + 17}{(x + 8) - 1}$

$\sf \Longrightarrow \dfrac{3}{2} = \dfrac{x + 17}{x + 7}$

by Cross Multiply -

$\sf \Longrightarrow 2(x + 17) = 3(x + 7)$

$\sf \Longrightarrow 2x + 34 = 3x + 21$

$\sf \Longrightarrow 34 − 21 = 3x − 2x$

$\sf \Longrightarrow x=13$

Numerator of the rational number

= x = 13

Denominator of the rational number

= x + 8

= 13 + 8

= 21

Rational number = 13/21