Question

The numeraotor of a fraction is greater then its denomintor by 8 .If numerator is decreased by 17 and numerator is increase by 1 .The number obtained is 3/2 .Find the number .

Answer 1

$\huge\boxed{\mathtt\red{CORRECT\:QUESTION}}$

The numerator of a fraction is greater then its denomintor by 8 .If numerator is decreased by 17 and denominator is increase by 1 .The number obtained is 3/2 .Find the number.

$\huge\boxed{\mathtt\red{PROVIDED}}$

• numerator of the fraction is greater than its denominator by 8.

• If numerator is decreased by 17 and denominator is increase by 1 then the result is $\large{\mathtt{\frac{3}{2}}}$

$\huge\boxed{\mathtt\red{TO\:FIND}}$

• the required fraction.

$\huge\boxed{\mathtt\red{ASSUMPTION}}$

• Let the denominator of the fraction be x

• then, it's numerator is (x+8)

$\huge\boxed{\mathtt\green{SOLUTION}}$

According to the Question :-

$\large{\mathtt{⇒\:\frac{x+8-17}{x+1}=\frac{3}{2}}}$

$\large{\mathtt{⇒\:\frac{x-9}{x+1}=\frac{3}{2}}}$

• By cross ❌ multiplying :-

$\large{\mathtt{⇒\:2x-18=3x+3}}$

$\large{\mathtt{⇒\:3x-2x=-18-3}}$

$\large{\mathtt{∴x=-21}}$

$\huge\boxed{\mathtt\green{ANSWER}}$

∴ The required fraction is :

⇒ $\large\boxed{\mathtt\green{\:\frac{x+8}{x}=\frac{-13}{-21}=\frac{13}{21}}}$

Answer 2

Given:

• numerator of the fraction is greater than

its denominator by 8.

• If numerator is decreased by 17 and

denominator is increase by 1 then the result is

$\frac{3}{2}$

FIND:

the required fraction.

ASSUMPTION:

• Let the denominator of the fraction be x

• then, it's numerator is (x+8)

SOLUTION:

According to the Question :-

→ $\frac{x + 8 - 17}{x + 1} = \frac{3}{2}$

→ $\frac{x - 9}{x - 1} = \frac{3}{2}$

By cross X multiplying :

⇒ 2x-18 = 3x + 3

→ 3x-2x= -18-3

→ x = -21

ANSWER:

The required fraction is :

$→ \frac{ x + 8}{x} = \frac{ - 13}{ - 21} = \frac{13}{21}$