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. 
\[ \frac{Q_A-Q_B}{Q_B}\times100 = \frac{2Q_B-Q_B}{Q_B}\times100 = 100\%. \] \[ \boxed{100\%} \]

Answer 2

Assuming convenient concrete values for price and quantity, instead of working purely with symbols, gives a quick alternate check.

1. 50%: With \(P_B=100\), \(P_A=75\), and \(Q_B=100\), a 50% increase gives \(Q_A=150\), so revenue from A is \(75\times150=11250\), while \(1.5\times\)revenue from B\(=1.5\times10000=15000\). These don't match, so 50% is too small.
2. 75%: Here \(Q_A=175\), giving revenue \(75\times175=13125\), still short of the required 15000.
3. 100%: Here \(Q_A=200\), giving revenue \(75\times200=15000\), exactly matching \(1.5\times10000=15000\).
4. 125%: Here \(Q_A=225\), giving revenue \(75\times225=16875\), overshooting the required 15000.

With B's price and quantity both taken as 100 for convenience, A's price is \(75\) (25% less). For A's revenue to be \(1.5\) times B's revenue of \(10000\), i.e. \(15000\), A's quantity must be \(15000/75=200\), which is exactly double B's quantity of 100, i.e. 100% more.

So the correct answer is 100%.