On decreasing the price of T. V. sets by `30%`. Its sale is increased by` 20%`. Whatis the effect on the revenue received by the shopkeeper?

Options

A. `10%` increase
B. `10%` decrease
C. `16%` increase
D. `16%` decrease

Answer

To solve the problem of how the revenue of the shopkeeper is affected by a decrease in the price of T.V. sets by 30% and an increase in sales by 20%, we can follow these steps:

### Step 1: Define the initial conditions
Let’s assume the initial price of the T.V. set is \( P \) and the initial number of T.V. sets sold is \( Q \).

### Step 2: Calculate the initial revenue
The initial revenue \( R_1 \) can be calculated using the formula:
\[ R_1 = P \times Q \]

### Step 3: Calculate the new price after a 30% decrease
The new price \( P' \) after a 30% decrease can be calculated as:
\[ P' = P - (30\% \text{ of } P) = P - 0.3P = 0.7P \]

### Step 4: Calculate the new quantity sold after a 20% increase
The new quantity \( Q' \) sold after a 20% increase can be calculated as:
\[ Q' = Q + (20\% \text{ of } Q) = Q + 0.2Q = 1.2Q \]

### Step 5: Calculate the new revenue
The new revenue \( R_2 \) can be calculated using the new price and new quantity:
\[ R_2 = P' \times Q' = (0.7P) \times (1.2Q) = 0.84PQ \]

### Step 6: Determine the effect on revenue
Now, we can compare the new revenue \( R_2 \) with the initial revenue \( R_1 \):
\[ R_1 = PQ \]
\[ R_2 = 0.84PQ \]

### Step 7: Calculate the change in revenue
To find the change in revenue, we can calculate:
\[ \text{Change in Revenue} = R_2 - R_1 = 0.84PQ - PQ = -0.16PQ \]

### Step 8: Calculate the percentage change in revenue
To find the percentage change in revenue:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Revenue}}{R_1}\right) \times 100 = \left(\frac{-0.16PQ}{PQ}\right) \times 100 = -16\% \]

### Conclusion
The revenue received by the shopkeeper decreases by **16%**.

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