Question

The ratio of the numerator to the denominator of a certain fraction is three to five. If two is added to the numerator and

Answer 1

Answer:

The original fraction is  $\frac{3}{5}$

Step-by-step explanation:

Given as :

The ratio of numerator to denominator = 3 : 5

Let The numerator = 3 x

Let The denominator = 5 x

Again

If two is added to the numerator and  five is subtracted from the denominator, the new fraction reduces to four fifths.

So, $\dfrac{3 x + 2}{5 x - 5}$ = $\frac{4}{5}$

Or, 5 × (3 x + 2) = 4 × (5 x - 5)

Or, 15 x + 10 = 20 x - 20

Or, 20 x - 15 x = 10 + 20

or, 5 x = 30

∴  x = $\frac{30}{5}$

i.e x = 6

So, The numerator = 3 × 6 = 18

And The denominator = 5 × 6 = 30

∴ Original fraction = $\frac{numerator}{denominator}$

Or, Original fraction = $\frac{18}{30}$ = $\frac{3}{5}$

Hence, The original fraction is  $\frac{3}{5}$  Answer