Question

A company produces two articles, A and B. The per unit price of A is 25\% less than the per unit price of B. By what percent is the sales (units) of A more than the sales of B if the revenue earned from A is 1.5 times the total revenue earned from B?

• A. 50\%
• B. 75\%
• C. 100\%
• D. 125\%

Hint:

When comparing sales from revenue, set \(R=P\times Q\). If one price is a known percent of the other, cancel the common factor to get the ratio of quantities directly.

Answer 1

The Correct Option is C

Step 1: Translate prices.
Let \(P_B\) be B's price and \(P_A=0.75P_B\) (25\% less). Step 2: Use the revenue relation.
Let \(Q_A,Q_B\) be units sold. Given revenue \(R_A=1.5R_B\):
\[ P_AQ_A = 1.5\,P_BQ_B \quad \Rightarrow \quad 0.75P_B\,Q_A = 1.5P_B\,Q_B. \] Cancel \(P_B > 0\): \(\ 0.75Q_A = 1.5Q_B \Rightarrow Q_A/Q_B = 2.\) Step 3: Percent by which A's sales exceed B's.
\[ \frac{Q_A-Q_B}{Q_B}\times100 = \frac{2Q_B-Q_B}{Q_B}\times100 = 100\%. \] \[ \boxed{100\%} \]