Question

the numerator of a fraction is 5 less than its denominator.
if 3 is added to its numerator and denominator both, the fraction becomes 4/5
find the original fraction.​

Answer 1

Answer:

The original fraction is 17/22.

Step-by-step explanation:

Consider the provide information.

As per the provided information in the given question, we've been given that, the numerator of a fraction is 5 less than its denominator and if 3 is added to its numerator and denominator both, the fraction becomes 4/5. With this information, we have been asked to find out the original fraction.

Let us assume that x be the denominator of the fraction. Then numerator be x - 5.

So, original fraction be x - 5/x.

As it is given that, if 3 is added to its numerator and denominator both, the fraction becomes 4/5. So,

→ [(x - 5 + 3)/(x + 3)] = 4/5

→ [(x - 2)/(x + 3)] = 4/5

→ 5(x - 2) = 4x + 12

→ 5x - 10 = 4x + 12

→ 5x - 4x = 12 + 10

→ x = 12 + 10

→ x = 22

So, Original fraction = x - 5/x

Original fraction  = 22 - 5/22

Original fraction = 17/22

Hence, the original number is 17/22.

#Learn more:

1. The sum of the numerator and denominator of a certain fraction is 8. If 2 is added to the numerator and to the denominator, the value of the fraction increased by 4/35. Find the fraction.

- brainly.in/question/27795417

2. The denominator of a rational number is 1 greater than its numerator if the numerator is increased by 17 and the denominator is decreased by 1 the number becomes 27 find the rational number.

- brainly.in/question/25315582

Answer 2

Answer:

Given :-

• The numerator of a fraction is 5 less than its denominator.
• 3 is added to its numerator and denominator both, the fraction becomes 4/5.

To Find :-

• What is the original fraction.

Solution :-

Let,

$\leadsto \sf Numerator =\: a$

$\leadsto \sf Denominator =\: b$

Hence, the fraction will be :

$\leadsto \bf Original\: Fraction =\: \dfrac{a}{b}$

According to the question,

$\bigstar$ The numerator of a fraction is 5 less than its denominator.

$\small \implies \bf \bigg\{Numerator\bigg\} =\: \bigg\{Denominator - 5\bigg\}$

$\implies \sf a =\: b - 5$

$\implies \sf\bold{\purple{a =\: b - 5\: ------\: (Equation\: No\: 1)}}$

Again,

$\bigstar$ If 3 is added to its numerator and denominator both, the fraction becomes 4/5.

$\implies \bf \bigg\{\dfrac{Numerator + 3}{Denominator + 3}\bigg\} =\: \bigg\{\dfrac{4}{5}\bigg\}$

$\implies \sf \dfrac{a + 3}{b + 3} =\: \dfrac{4}{5}$

By doing cross multiplication we get,

$\implies \sf 5(a + 3) =\: 4(b + 3)$

$\implies \sf 5a + 15 =\: 4b + 12$

$\implies \sf 5a - 4b =\: 12 - 15$

$\implies \sf\bold{\purple{5a - 4b =\: - 3\: ------\: (Equation\: No\: 2)}}$

By putting a = b - 5 in the equation no 2 we get,

$\implies \sf 5a - 4b =\: - 3$

$\implies \sf 5(b - 5) - 4b =\: - 3$

$\implies \sf 5b - 25 - 4b =\: - 3$

$\implies \sf 5b - 4b =\: - 3 + 25$

$\implies \sf\bold{\green{b =\: 22}}$

Again, by putting b = 22 in the equation no 1 we get,

$\implies \sf a =\: b - 5$

$\implies \sf a =\: 22 - 5$

$\implies \sf\bold{\green{a =\: 17}}$

Hence, the required original fraction will be :

$\dashrightarrow \sf Original\: Fraction =\: \dfrac{a}{b}$

$\dashrightarrow \sf\boxed{\bold{\red{Original\: Fraction =\: \dfrac{17}{22}}}}$

$\therefore$ The original fraction is 17/22 .

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