Question

the numertor of a fraction is 2 less than the denominator if 3 is added to both the numertor ant the denominator the fraction become 3/4 find the fraction​

Answer 1

Solution:-

Let the denominator be x

So numerator is 2 less than denominator

Equation is

$\rm \: \dfrac{x - 2}{x}$

Now

3 is added in both numerator and denominator

$\rm \: \dfrac{x - 2 + 3}{x + 3}$

Now fraction is increased by 3/4

$\rm \dfrac{x - 2 + 3}{x + 3} = \dfrac{3}{4}$

$\rm \dfrac{x + 1}{x + 3} = \dfrac{3}{4}$

Using cross multiplication

$\rm \: 4(x + 1) = 3(x + 3)$

$\rm4x + 4 = 3x + 9$

$\rm \: x = 5$

Now fraction is

$\rm \dfrac{5 - 2}{5} = \dfrac{3}{5}$

Answer 2

Question:-

The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator the fraction become 3/4 find the fraction.

Answer:-

Let the denominator be x

Then the numerator will be x -2

Hence, the original fraction can be written as (x - 2)/x

→ Original fraction = (x - 2)/x

When 3 is added to both numerator and denominator, then the new fraction will be (x - 2 + 3)/(x + 3)

→ New fraction = (x - 2 + 3)/(x + 3)

→ New fraction = (x + 1)/(x + 3)

Given: New fraction is equal to 3/4

A/q

New fraction = 3/4

→ (x + 1)/(x + 3) = 3/4

→ 4(x + 1) = 3(x + 3)

→ 4x + 4 = 3x + 9

→ 4x - 3x = 9 - 4

→ x = 5

We know, Original fraction = (x - 2)/x

→ Original fraction = (5 - 2)/(5)

→ Original fraction = 3/5

Ans. Original fraction = 3/5