A fraction becomes \(\frac{6}{5}\) when 5 is added to its numerator and becomes \(\frac{1}{2}\) when 4 is added to its denominator. The fraction is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{7}{10}\)
Let the fraction be \(\frac{x}{y}\). Each condition gives one equation, and the two are solved together.
The two conditions:
\(\displaystyle\frac{x+5}{y}=\frac{6}{5}\), so \(5x+25=6y\) (1)
\(\displaystyle\frac{x}{y+4}=\frac{1}{2}\), so \(y=2x-4\) (2)
Putting (2) into (1):
\(5x+25=12x-24\), so \(7x=49\) and \(x=7\)
From (2): \(y=14-4=10\)
Shortcut: Test the options in the second condition, which is quicker: only \(\frac{7}{10}\) gives \(\frac{7}{14}=\frac{1}{2}\) when 4 is added to the denominator (\(\frac{8}{13}\), \(\frac{7}{12}\) and \(\frac{6}{15}\) do not).