Question

18. In a fraction, twice the numerator is 2 more than the
denominator. If 3 is added to the numerator and to
the denominator, the new fraction is 2upon3.Find the
original fraction.​

Answer 1

What to do?

Find the original fraction.

How to do?

To find the original fraction, we have to form the equation from question and solve it.

Solution:

Let x be the numerator of the fraction.

Hence, its denominator will 2x - 2.

So, the fraction will be  $\frac{x}{2x-2}$.

As stated in the question,

The numerator will be x + 3.

The denominator will be 2x - 2 + 3.

So, the new fraction will be $\frac{x+3}{2x-2+3} = \frac{x+3}{2x+1}=\frac{2}{3}$.

The equation will be,

⇒ $\frac{x+3}{2x+1} = \frac{2}{3}$  

First cross multiply the fraction,

⇒ 3(x + 3) = 2(2x + 1)

Next remove the brackets,

⇒ 3x + 9 = 4x + 2

Then shift 2 to RHS and 3x to LHS,

⇒ 9 - 2 = 4x - 3x

Then solve the RHS and LHS,

⇒ 7 = x

To find the original fraction, substitute the value,

Numerator = x = 7

Denominator = 2x - 2 = 2(7) - 2 = 14 - 2 = 12

∵ So, the original fraction is 7/12.