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If the numerator of a fraction is increased by 100% and the denominator is increased by 150%, then the fraction becomes 1625\frac{16}{25}2516​​. What
Question

If the numerator of a fraction is increased by 100% and the denominator is increased by 150%, then the fraction becomes 1625\frac{16}{25}​. What is the original fraction?

A.

​512\frac{5}{12}​​

B.

​45\frac{4}{5}​​

C.

​712\frac{7}{12}​​

D.

​56\frac{5}6​​

Correct option is B

Given:
​Numerator is increased by 100%.
Denominator is increased by 150%.
New fraction becomes 1625.\frac{16}{25}.  ​
Solution: 
​Let say the fraction is xy.According to the question,x+100100xy+150100y=1625.or, 2x2.5y=1625.or, xy=1625×2.52=810=45.\text{Let say the fraction is } \frac{x}{y}. \\\text{According to the question,} \\\frac{x + \frac{100}{100}x}{y + \frac{150}{100}y} = \frac{16}{25}. \\\text{or, } \frac{2x}{2.5y} = \frac{16}{25}. \\\text{or, } \frac{x}{y} = \frac{16}{25} \times \frac{2.5}{2} = \frac{8}{10} = \frac{4}{5}.​​

Thus, the original fraction is 45\frac{4}{5}.​

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