Question

"The denominator of a fraction is 5 more than the numerator. If the numerator is increased by 18 and thedenominator is decreased by 4, the fraction becomes
$\frac{25}{8}$
Find the fraction
​

Answer 1

Answer:

Given :-

• The denominator of a fraction is 5 more than the numerator. If the numerator is increased by 18 and the denominator is decreased by 4, the fraction becomes 25/8.

To Find :-

• What is the fraction.

Solution :-

Let, the numerator be x

And, the denominator will be x + 5

Then, the fraction will be $\sf\dfrac{x}{x + 5}$

According to the question,

⇒ $\sf\dfrac{x + 18}{(x + 5) - 4} =\: \dfrac{25}{8}$

⇒ $\sf\dfrac{x + 18}{x + 1} =\: \dfrac{25}{8}$

By doing cross multiplication we get,

⇒ $\sf 8(x + 18) =\: 25(x + 1)$

⇒ $\sf 8x + 144 =\: 25x + 25$

⇒ $\sf 8x - 25x =\: 25 - 144$

⇒ $\sf - 17 =\: - 119$

⇒ $\sf x =\: \dfrac{\cancel{- 119}}{\cancel{- 17}}$

➠ $\sf\bold{x =\: 7}$

Hence, the required fraction are,

↦ $\sf\dfrac{x}{x + 5}$

↦ $\sf\dfrac{7}{7 + 5}$

➤ $\sf\red{\dfrac{7}{12}}$

$\therefore$ The fraction is $\sf\boxed{\bold{\large{\dfrac{7}{12}}}}$.

$\rule{300}{1.5}$

Let's Verify :-

↪ $\sf\dfrac{x + 18}{(x + 5) - 4} =\: \dfrac{25}{8}$

↪ $\sf\dfrac{x + 18}{x + 1} =\: \dfrac{25}{8}$

Put x = 7 we get,

↪ $\sf\dfrac{7 + 18}{7 + 1} =\: \dfrac{25}{8}$

↪ $\sf\dfrac{25}{8} =\: \dfrac{25}{8}$

➦ LHS= RHS

Hence, Verified ✔

Answer 2

Given:

✰ The denominator of a fraction is 5 more than the numerator.

✰ The numerator is increased by 18 and the denominator is decreased by 4, the fraction becomes 25/8

To find:

✠ The fraction

Solution:

Let the numerator be x

We know, that the denominator of a fraction is 5 more than the numerator, so we will add 5 to numerator.

Then, the denominator be x + 5

Now, we know that if the numerator is increased by 18 i.e., adding 18 to the numerator and the denominator is decreased by 4 i.e, substracting 4 from the denominator, we will get fraction 25/8.

According to the problem,

$\\ \\ \implies{ \sf{ \dfrac{x + 18}{(x + 5) - 4} = \dfrac{25}{8}}}$

$\implies{ \sf{ \dfrac{x + 18}{x + 5 - 4} = \dfrac{25}{8}}}$

$\implies{ \sf8(x + 18) = 25(x + 1)}$

$\implies{ \sf8x + 144 = 25x + 25}$

$\implies{ \sf 144 - 25 = 25x - 8x}$

$\implies{ \sf 119 = 17x}$

$\implies{ \sf{x = \dfrac{119}{17}}}$

$\implies{ \sf{x = \dfrac{ {\cancel{119}}^{7} }{ \cancel{17}}}}$

$\implies{ \sf{x = 7}}$

Numerator = x = 7

Denominator = x + 7 = 12

The Fraction is $\\ \\ \green{\large{ \underline{ \boxed{ \sf{\dfrac{7}{12}}}}}}$

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