Question

A radio is sold for Rs 3120 at a loss of 4%. What will be the gain or loss per cent if it is sold for Rs 3445?

Answer 1

Let the original price be $x$.
SP = Rs 3120
Now, SP = CP − loss
​$$\begin{gathered} \Rightarrow 3120=x-\frac{4}{{\displaystyle \frac{100}{x}}} \\ \Rightarrow 3120=x-\frac{x}{25} \\ \Rightarrow 3120=\frac{24x}{25} \\ \Rightarrow \frac{3120\times 25}{24}=x \\ \Rightarrow x=3250 \end{gathered}$$

So, the cost price is Rs 3250.

If it is sold for Rs 3445, then its a gain because SP > CP.
Now, gain = SP − CP
= Rs (3445 − 3250)
= Rs 195
$$\begin{gathered} \therefore Gainpercentage=\left(\frac{gain}{CP}\times 100\right)\% \\ =\left(\frac{195}{3250}\times 100\right)\% \\ =6\% \end{gathered}$$

Hence, gain percent = 6%