What is the ratio between the marked price of two identical items, P and Q, which had been purchased at the same price? I. Item P was sold at a profit of 20%, while item Q was sold at a loss of 10%. II. Item P was sold at a discount of 4%. The percentage by which Item Q’s cost price been marked up is 2.5 times the profit % earned on selling item P. III. The overall profit earned on selling items P and Q was 5%.

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Let the common cost price be $C$. From statement I: item P sold at 20% profit and Q sold at 10% loss, so

- $S_P=1.2C$
- $S_Q=0.9C$

From statement II: P was sold at a 4% discount, so

- $S_P=0.96M_P\Rightarrow M_P=\dfrac{S_P}{0.96}=\dfrac{1.2C}{0.96}=1.25C$.

Statement II also says Q's markup% on cost is $2.5$ times the profit% earned on P. The profit% on P is $20\%$, so Q's markup% = $2.5	imes20\%=50\%$, hence

- $M_Q=1.5C$.

Therefore the ratio of marked prices is

$M_P:M_Q=1.25C:1.5C=5:6$,

which is uniquely determined by combining I and II. Individually each statement is insufficient (I gives selling results but not marked prices; II depends on P's profit% which I supplies). Thus statements I and II together suffice to find the required ratio.

FINAL_ANSWER: a

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