A1 By how much percent does the value of a fraction change if its numerator is increased by $5 \%$ and its denominator by $20 \%$?
(A) increases by $25 \%$
(B) decreases by $12.5 \%$
(C) remains the same
(D) decreases by $25 \%$
(E) increases by $12.5 \%$
A1. Let the original fraction be $\frac{a}{b}$. If we increase the numerator by $5\%$ and the denominator by $20\%$, the new fraction becomes $\frac{1.05a}{1.2b}$, which is $0.875$ of $\frac{a}{b}$. Therefore, the new fraction decreases by $12.5\%$.