Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the
the fraction is equal to 2/
3. Find the orignal fraction


Those who will answer I will mark them as the brainliest answers​

Answer 1

CORRECT QUESTION:

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator the fraction is equal to 2/3. Find the original fraction.

GIVEN:

• The numerator of a fraction is 6 less than the denominator.
• If 3 is added to the numerator the fraction is equal to 2/3.

TO FIND:

• What is the original fraction ?

SOLUTION:

Let the original fraction be $\bf{\dfrac{x}{y}}$

We have given that the numerator of a fraction is 6 less than the denominator

According to question:-

$\bf{ \mapsto x = y - 6...1)}$

★ If 3 is added to the numerator the fraction is equal to 2/3

According to question:-

$\rm{\mapsto \dfrac{x + 3}{y} = \dfrac{2 }{3}}$

Use cross product:

$\rm{\mapsto 3(x + 3) = 2y}$

$\rm{\mapsto 3x + 9 = 2y...2)}$

Put the value of 'x' from equation 1)

$\rm{\mapsto 3(y-6) + 9 = 2y}$

$\rm{\mapsto 3y- 18 + 9 = 2y}$

$\rm{\mapsto 3y - 2y = 18-9}$

$\bf{\mapsto \: \star \: y= 9 \: \star}$

Put the value of 'y' in equation 1)

$\rm{\mapsto x = 9-6}$

$\bf{\mapsto \: \star \: x = 3 \: \star}$

$\bf{ Original \: Fraction = \dfrac{x}{y} = \dfrac{3}{9}}$

____________________

VERIFICATION:

Put the value of 'x' and 'y' in equation 1)

➨ $\rm{ 3 = 9-6}$

➨ $\bf{ 3 = 3}$

Put the value of 'x' and 'y' in equation 2)

➨ $\rm{ 3 \times 3+ 9 = 2 \times 9}$

➨ $\rm{ 9 + 9 = 18}$

➨ $\bf{ 18 = 18}$

[L.H.S. = R.H.S.]

VERIFIED....