Question

When the price of the TV set was increased by 30%, then the number of TV sets sold decreased by 20%. What was the effect on sales?
(a) 5% decrease
(b) 7% increase
(c) 6% decrease
(d) 4% increase

Answer 1

Hint: Assume original price as ‘x’. Find the new price by adding ‘x’ with 30% of x. Now, assume the original number of TV sets sold as ‘y’. Find the new number of TV sets sold by subtracting 20% of y from ‘y’. Calculate the total original price by multiplying x and y and calculate the total new price by multiplying the new price with the new number of TV sets. Finally, subtract the total original price from the total new price to find a percentage increase or decrease. Find the percentage increase or decrease = (increase or decrease in total price)/ (total original price) \[\times 100%\].

Complete step-by-step solution:
Let us come to the question. We have been given that when the price of a TV set was increased by 30% then the number of TV sets sold decreased by 20%.
Let the original price of a TV set = x
\[\Rightarrow \] New price of the TV set = x + 30% of x
\[\Rightarrow \] New price of the TV set = \[x+\dfrac{30}{100}\times x\]
\[\Rightarrow \] New price of the TV set = 1.3x
Now, let the original number of TV sets sold = y
\[\Rightarrow \] New number of TV sets sold = \[y-\dfrac{20}{100}\times y\]
\[\Rightarrow \] New number of TV sets sold = \[y-\dfrac{y}{5}\]
\[\Rightarrow \] New number of TV sets sold = \[\dfrac{4y}{5}\]
\[\Rightarrow \] New number of TV sets sold = 0.8y
Therefore, we have,
Total original price of TV sets sold = original price \[\times \] number of TV sets sold
Total original price of TV sets sold = x \[\times \] y
Total original price of TV sets sold = xy
Total new price of TV sets sold = new price \[\times \] new number of TV sets sold
Total new price of TV sets sold = 1.3x \[\times \] 0.8y
The total new price of TV sets sold = 1.04xy
\[\Rightarrow \] Change in the sales = final price – original price
\[\Rightarrow \] Change in the sales = 1.04xy – xy
\[\Rightarrow \] Change in the sales = 0.04xy
Clearly, we can see that the change is positive. Therefore, there is an increase in sales.
\[\Rightarrow \] Percentage increase = (increase or decrease in total price)/ (total original price) \[\times 100%\]
\[\Rightarrow \] Percentage increase = \[\dfrac{0.04xy}{xy}\times 100%\]
\[\Rightarrow \] Percentage increase = 4%
Hence, option (d) is the correct answer.

Note: One may note that the change in the sales is positive, that means the final sale is greater than the initial sale. So, there is an increase or profit. If the change would have been negative then there would have been a loss or percentage decrease. Always remember that, while calculating percentage change we have to consider the original price in the denominator.