When the price of a cycle is decreased by 20%,then the selling is increased by 20%. What is the impact on the receipt of the revenue?

Options

A. a) 4% loss
B. b) 5% profit
C. c) No profit no loss
D. d) 4% profit

Answer

To solve the problem, we need to determine the net impact on revenue when the price of a cycle is decreased by 20% and the quantity sold is increased by 20%. We can use the formula for net impact in percentage terms.

### Step-by-Step Solution:

1. **Identify the Changes**:
- Let the original price of the cycle be \( P \).
- The price is decreased by 20%, so the new price \( P' \) is:
\[ P' = P - 0.20P = 0.80P \]
- The quantity sold is increased by 20%. If the original quantity sold is \( Q \), the new quantity sold \( Q' \) is:
\[ Q' = Q + 0.20Q = 1.20Q \]

2. **Calculate Original Revenue**:
- The original revenue \( R \) is given by:
\[ R = P \times Q \]

3. **Calculate New Revenue**:
- The new revenue \( R' \) after the changes is:
\[ R' = P' \times Q' = (0.80P) \times (1.20Q) \]
- Simplifying this:
\[ R' = 0.80 \times 1.20 \times P \times Q = 0.96PQ \]

4. **Determine the Impact on Revenue**:
- The impact on revenue can be calculated as:
\[ \text{Impact} = R' - R = 0.96PQ - PQ = -0.04PQ \]
- To express this as a percentage of the original revenue:
\[ \text{Percentage Impact} = \left(\frac{-0.04PQ}{PQ}\right) \times 100 = -4\% \]

5. **Conclusion**:
- The net impact on the revenue is a decrease of 4%. This indicates a loss in revenue.

### Final Answer:
The impact on the receipt of the revenue is a decrease of **4%**.

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