If numerator of fraction is increased by 150% and denominator is increased by 50% the resultant fraction becomes \(\frac{15}{16}\). What was the original fraction?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{9}{16}\)
A 150% increase makes a quantity \(100\%+150\%=250\%\) of itself, that is 2.5 times; a 50% increase makes it 1.5 times. Let the original fraction be \(\frac{x}{y}\); only the numerator and the denominator change, so the new fraction is a fixed multiple of the old one.
The new fraction is \(\displaystyle \frac{2.5x}{1.5y}=\frac{5}{3}\times\frac{x}{y}\)
It is given to be \(\frac{15}{16}\): \(\displaystyle \frac{5}{3}\times\frac{x}{y}=\frac{15}{16}\)
So the original fraction is \(\displaystyle \frac{x}{y}=\frac{15}{16}\times\frac{3}{5}=\frac{9}{16}\)