Re: The revenue collected from selling television sets in a certain stor
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06 Dec 2024, 14:31
We know that there was a decrease of $\(20 \%\)$ in the number of televisions sold; we need to check the percentage by which the price of television must be increased to have unchanged revenue. where \(revenue\) $\(=\)$ \(Price $\times$ Quantity\).
It is known that when A is a result of product of two things, say $\(\mathrm{P}\) & \(\mathrm{Q}\)$ and if the quantity P is increased/decreased by say $\(x \%\)$ then the quantity $Q$ need to be changed by $\(\frac{100 x}{(100 \pm x)} \%\)$ so that $\(A\)$ remains constant $\(((+)\)$ sign will come in denominator when there is an increase in $\(P\)$ and in case of decrease in $\(\mathrm{P},(-)\)$ sign will be there in denominator).
As the 'Revenue $=$ Price $\times$ Quantity' and the number of televisions (Quantity) sold decreased by $\(20 \%\)$, the price of the television must be increased by $\(\frac{100 \times 20}{(100-20)} \%=\frac{20}{80} \times 100=25 \%\)$ so that the revenue remains constant.
Hence the answer is (C).