Question

If the selling price were to be increased by $10%$, the sales would reduce by $10%$. In what ratio would profits change?
I. The cost price remains constant.
II. The cost price increased $10%$.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both statements I and II are needed to answer the question.
• D. If the question cannot be answered even with the help of both statements.

Hint:

In profit comparison problems, changes in selling price and cost price must be applied carefully to both unit profit and quantity sold before finding ratios.

Answer 1

The Correct Option is A

Let the original selling price be $S$ and the original quantity sold be $Q$. Let the cost price be $C$ (per unit).
Original profit: \[ P_1 = (S - C) \times Q \] After the $10%$ increase in selling price, new selling price is: \[ S' = 1.1S \] Sales quantity reduces by $10%$, so: \[ Q' = 0.9Q \] New profit (per unit) = $(S' - C)$ if cost price remains constant.
Thus: \[ P_2 = (1.1S - C) \times 0.9Q \] The ratio of profits is: \[ \frac{P_2}{P_1} = \frac{(1.1S - C) \times 0.9Q}{(S - C) \times Q} = 0.9 \times \frac{1.1S - C}{S - C} \] From Statement I (cost price constant), we can calculate this ratio exactly if $S$ and $C$ relation is known. Without $S$ and $C$ values, the exact numerical ratio cannot be computed — but if the question implies "ratio in terms of $S$ and $C$" then Statement I is enough.
From Statement II (cost price increased by $10%$), the situation changes: $C' = 1.1C$, and profit ratio changes accordingly. Without original $C$, still no numeric answer.
Therefore, only Statement I gives a fixed relationship allowing the profit ratio calculation, so correct answer is (a).