Question

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

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Answer 1

Answer :-

The fraction is 13/21.

Step-by-step explanation:

To Find :-

• The fraction.

★ Solution

Given,

Denominator of a fraction is greater than the numerator by 8.

Therefore, Let us assume the numerator as (x) and denominator as (x + 8).

The fraction is $\bf{\dfrac{x}{(x + 8)}}$

Also given, The numerator is increased by 17. The Denominator is decreased by 1. And the fraction or number obtained is 3/2.

Hence, The new numerator and denominator is :-

Numerator :-

⇒ (x) + 17

⇒ (x + 17)

Denominator :-

⇒ (x + 8) - 1

⇒ (x + 7)

According the question,

Given, The fraction: $\boxed{\sf{\dfrac{(x + 17)}{(x + 7)} = \dfrac{3}{2}}}$

By simplifying,

$\sf{\mapsto \: \dfrac{(x + 17)}{(x + 7)} = \dfrac{3}{2}}$

By cross multiplication,

$\sf{\longmapsto \: 3(x + 7) = 2(x + 17)}$

$\sf{\longmapsto \: 3(x + 7) = 2(x + 17)}$

$\sf{\longmapsto \: 3x + 21 = 2x + 34}$

$\sf{\longmapsto \: 3x = 2x + 34 - 21}$

$\sf{\longmapsto \: 3x = 2x + 13}$

$\sf{\longmapsto \: 3x - 2x = 13}$

$\sf{\longmapsto \: x = 13}$

The value of x is 13.

Now, The fraction is :-

We assumed the numerator and denominator as (x) and (x + 8).

$\sf{\longmapsto \: \dfrac{(x)}{(x + 8)}}$

$\sf{\longmapsto \: \dfrac{13}{(13 + 8)}}$

$\bf{\longmapsto \: \dfrac{13}{21}}$

Hence, The fraction is 13/21.

Answer 2

Answer:

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