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
five is subtracted from the denominator, the new fraction reduces to four fifths. Find the onginal fraction

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