Question

If the numerator and denominator of a fraction are in the ratio 3:4 and it reduces to 1/5 on subtracting 4 from the Numerator. Find the Fraction.

Answer 1

Hi !!!

This is your answer.

Given :-

Numerator and Denominator are in ratio 3:4.
If 4 is subtracted from Numerator, it becomes 1/5.

Let the common ratio be k.

So.....
$\frac{3k \: - 4}{4k} = \frac{1}{5}$
Cross multiplying.. ..
4k = 5(3k-4)
4k = 15k - 20
15k - 4k = 20
11k = 20
k = 20/11.

Common ratio is 20/11.

Hence Numerator = 3× 20/11 = 60/11.
Denominator = 4 × 20/11 = 80/11.

Therefore.....

$fraction \: = \: \frac{ \frac{60}{11} }{ \frac{80}{11} } \\ = \frac{60}{11} \times \frac{11}{80} \\ = \frac{6}{8} = \frac{3}{4}$
Hence the fraction is 3/4.

Hope it helps