If the price of an article is increased by `25%` the number of articles sold is reduced by `22%` . What will be the effect on revenue?

Options

A. `2.5%` increase
B. `2.5%` decrease
C. `1.5%` increase
D. `1.5%` decrease

Answer

To determine the effect on revenue when the price of an article is increased by 25% and the number of articles sold is reduced by 22%, we can follow these steps:

### Step 1: Define the initial price and quantity
Let the initial price of the article be \( P \) and the initial quantity sold be \( Q \).

### Step 2: Calculate the new price after the increase
The price is increased by 25%, so the new price \( P' \) can be calculated as:
\[ P' = P + 0.25P = 1.25P \]

### Step 3: Calculate the new quantity sold after the decrease
The quantity sold is reduced by 22%, so the new quantity \( Q' \) can be calculated as:
\[ Q' = Q - 0.22Q = 0.78Q \]

### Step 4: Calculate the initial revenue
The initial revenue \( R \) is given by:
\[ R = P \times Q \]

### Step 5: Calculate the new revenue after the changes
The new revenue \( R' \) can be calculated as:
\[ R' = P' \times Q' = (1.25P) \times (0.78Q) = 0.975PQ \]

### Step 6: Calculate the percentage change in revenue
To find the percentage change in revenue, we can use the formula:
\[ \text{Percentage Change} = \left( \frac{R' - R}{R} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \left( \frac{0.975PQ - PQ}{PQ} \right) \times 100 = \left( \frac{-0.025PQ}{PQ} \right) \times 100 = -2.5\% \]

### Conclusion
The revenue decreases by 2.5%.