Question

If the price of silk is reduced by 20%, its consumption increased by 30%. By what percent revenue increases or decreases:

Answer 1

To determine the effect of a price reduction and an increase in consumption on revenue, we can use a general approach by denoting the initial price and quantity.

Let's denote:
- \( P \): original price of silk
- \( Q \): original quantity consumed

The original revenue \( R \) can be calculated as:
\[
R = P \times Q
\]

After a 20% decrease in price, the new price \( P' \) becomes:
\[
P' = P \times (1 - 0.20) = P \times 0.80
\]

At the same time, the consumption increases by 30%, making the new quantity \( Q' \):
\[
Q' = Q \times (1 + 0.30) = Q \times 1.30
\]

Now, we can calculate the new revenue \( R' \):
\[
R' = P' \times Q' = (P \times 0.80) \times (Q \times 1.30) = P \times Q \times 0.80 \times 1.30
\]

Now, compute the new revenue:
\[
R' = R \times 0.80 \times 1.30
\]

Calculating \( 0.80 \times 1.30 \):
\[
0.80 \times 1.30 = 1.04
\]

Thus, the new revenue \( R' \) is:
\[
R' = R \times 1.04
\]

This means the revenue increases. To find the percentage increase in revenue:
\[
\text{Percentage Increase} = \left( \frac{R' - R}{R} \right) \times 100 = \left( \frac{R \times 1.04 - R}{R} \right) \times 100 = (1.04 - 1) \times 100 = 0.04 \times 100 = 4\%
\]

Thus, the revenue increases by **4%**.