Question

If the numerator of fraction is increased by 50% and the denominator is increased by 300% , the resultant fraction is 2 . What was the original fraction?

Answer 1

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Answer 2

Given: If the numerator of fraction is increased by 50% and the denominator is increased by 300% , the resultant fraction is 2.

To find: The original fraction

Solution: Let the numerator be p and the denominator be q.

Therefore, original fraction

$= \frac{p}{q}$

The numerator is increased by 50%, therefore

New numerator

= p + 50% of p

= p + (50/100) × p

= p + 0.5 p

= 1.5 p

The denominator is increased by 300%, therefore

New denominator

= q + 300% of q

= q + (300/100)×q

= q+3q

= 4q

Therefore, the new fraction

$= \frac{1.5p}{4q}$

But the new fraction is equal to 2.

Therefore,

$= > \frac{1.5p}{4q} = 2$

$= > \frac{p}{q} = \frac{2 \times 4}{1.5}$

$= > \frac{p}{q} = \frac{8}{1.5}$

$= > \frac{p}{q} = \frac{80}{15}$

$= > \frac{p}{q} = \frac{16}{3}$

Therefore, the original fraction was 16/3.