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.what is the original fraction equal to?​

Answer 1

Answer:

First of all, we need to frame equations in accordance with the given parameters and information.

GiveN:

• Numerator is 6 less than the denominator.
• 3 is added to the numerator, the fraction is equal to 2/3.

We have to find the original fraction.

Let's consider:

Numerator be x and denominator be y. According to first condition, y is greater than x by 6.

➝ y = x + 6

➝ y - x = 6 -------(1)

And the fraction would be

➝ x / y

Now according to second condition, if 3 is added to the numerator, then fraction will become 2/3.

➝ x + 3 / y = 2/3

Cross multiplying,

➝ 3(x + 3) = 2y

➝ 3x + 9 = 2y

➝ 2y - 3x = 9 ------(2)

Multiplying eq. (1) with 2,

➝ 2(y - x) = 12

➝ 2y - 2x = 12

Now subtracting eq. (2) from eq. (1),

➝ 2y - 2x - (2y - 3x) = 12 - 9

➝ 2y - 2x - 2y + 3x = 3

➝ x = 3

Then, y = 9

So, the original fraction is:

$\large{ \boxed{ \tt{ \red{ \frac{3}{9}}}}}$

And we are done !!