Question

than twice the number.
10. The numerator of a fraction is 5 less than its
denominator. If 3 is added to the numerato
and denominator both, the fraction become
4
Find the original fraction.
5​

Answer 1

CORRECT QUESTION.

The numerator of a fraction is 5 less than it's

denominator. if 3 is added to the numerator

and denominator both the fraction become

4/5. find the original fraction.

EXPLANATION.

Let the numerator of a fraction = x - 5

Let the denominator of a fraction = x

Fraction = x - 5 / x

If 3 is added to both numerator and denominator.

fraction become 4/5.

=> x - 5 + 3 / x + 3 = 4/5

=> x - 2 / x + 3 = 4/5

=> 5 ( x - 2 ) = 4 ( x + 3 )

=> 5x - 10 = 4x + 12

=> x = 22

Therefore,

Fraction = x - 5 / x = 22 - 5 / 22 = 17 / 22

Answer 2

$\huge\mathcal{\underbrace{\red{QUESTION:-}}}$

✨ The numerator of a fraction is 5 less than it's denominator . If 3 is added to the numerator and denominator both then the fraction becomes 4/5 . Find the original fraction .

$\huge\mathcal{\underbrace{\red{ANSWER:-}}}$

$\mathcal{\gray{\underbrace{\blue{GIVEN:-}}}}$

• The numerator of a fraction is 5 less than it's denominator .

• If 3 is added to the numerator and denominator both then the fraction becomes 4/5 .

$\mathcal{\gray{\underbrace{\blue{TO\: FIND:-}}}}$

• The original fraction .

$\mathcal{\gray{\underbrace{\blue{SOLUTION:-}}}}$

Let,

• x be the numerator of a fraction .

• And y be the denominator of the fraction .

According to the question,

✍️ The numerator of a fraction is 5 less than it's denominator .

=> x = y - 5 ------(1)

⚡ If 3 is added to the numerator then the new numerator is “x + 3” .

⚡ And if 3 is added to the denominator then the new denominator is “y + 3” .

$\rm\red{\implies\:The\:new\:fraction\:=\:\dfrac{x\:+\:3}{y\:+\:3}\:}$

According to the question,

$\pink\checkmark\:\mathcal{\purple{\dfrac{x\:+\:3}{y\:+\:3}\:=\:\dfrac{4}{5}\:}}$

✍️ Put the value of “x = y - 5” in the above equation .

$\rm{\implies\:\dfrac{y\:-\:5\:+\:3}{y\:+\:3}\:=\:\dfrac{4}{5}\:}$

$\rm{\implies\:(y\:-\:2)\times{5}\:=\:(y\:+\:3)\times{4}\:}$

$\rm{\implies\:5y\:-\:10\:=\:4y\:+\:12\:}$

$\rm{\implies\:5y\:-\:4y\:=\:12\:+\:10\:}$

$\rm\green{\implies\:y\:=\:22\:}$

⚡ Put the value of “y = 2” in equation(1),

$\rm{\implies\:x\:=\:22\:-\:5\:}$

$\rm\green{\implies\:x\:=\:17\:}$

Hence,

• x/y = 17/22 .

$\red\bigstar\:\rm\underline{\gray{\boxed{\orange{\therefore\:The\:original\:fraction\:is\:\:\dfrac{17}{22}\:}}}}$