# Difficult Percentages Solved QuestionAptitude Discussion

 Q. The marks scored in History by $P,Q,R$ and $S$ form a geometric progression in that order. If the marks scored by $R$ were (dfrac{275}{9}%)less than the sum of the marks scored by $P$ and $Q$, then marks scored by $S$ were what percent more than the marks scored by $Q$? (Assume that everyone scored positive marks).
 ✔ A. $56.25 \%$ ✖ B. $55.55 \%$ ✖ C. $64 \%$ ✖ D. $67.75 \%$

Solution:
Option(A) is correct

Let the marks scored by $P,Q,R$ and $S$ be $a, ak, ak^2$ and $ak^3$ respectively.

Marks scored by $R$ were $\dfrac{275}{9}\%$  less than the marks scored by $P$ and $Q$.

So, if marks scored by $P$ and $Q$ were 36 then those scored by $R$ is 25.

Marks scored by $P$ and $Q =a+ak=36$

Marks scored by $R =ak^2=25$

$\Rightarrow \dfrac{(a+ak)}{a k^2}=\dfrac{36}{25}$

$\Rightarrow k=\dfrac{5}{4}$

$P=a,Q=\dfrac{5a}{4}, R=\dfrac{25a}{16}, S=\dfrac{125a}{64}$

$\Rightarrow P=64a$, $Q=80a$, $R=100a$ and $S=125a$

$S$ scored $\dfrac{125a-80}{80a}\times 100\%$more than $Q$

$\Rightarrow \dfrac{45}{80}\times 100$

$=56.25\%$

$S$ scored $56.25 \%$  more than $Q$.