Two hackers planned to hack a bank account which had debit card pin code in such a format that if a fraction could be made using the first two digits as numerator and last two digits as denominator, then if the numerator of the fraction was increased by 200% and the denominator by 300%, the fraction becomes 12/15. What was the pin of the debit card?
Solution
Correct Answer: Option E
n percent (%) of a number x = \(x \times \frac{n}{{100}}\)
Suppose the original fraction to be x/y.
Then, \(\frac{{x+x \times \frac{{200}}{{100}}}}{{y+y \times \frac{{300}}{{100}}}} = \frac{{12}}{{15}}\)
\(\Rightarrow \frac{x}{y} = \frac{{12 \times 4}}{{15 \times 3}}\)
\(\Rightarrow \frac{x}{y} = \frac{{16}}{{15}}\)
∴ Debit card pin is 1615
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