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?
Solution:
Let the original price be $x$.
SP = Rs 3120
Now, SP = CP - loss
$\Rightarrow 3120=x-\frac{4}{\frac{100}{x}}$
$\Rightarrow 3120=x-\frac{x}{25}$
$\Rightarrow 3120=\frac{24 x}{25}$
$\Rightarrow \frac{3120 \times 25}{24}=x$
$\Rightarrow x=3250$
So, the cost price is Rs 3250 .
If it is sold for Rs 3445 , then its a gain because $S P>C P$.
Now, gain = SP - CP
$=\operatorname{Rs}(3445-3250)$
= Rs 195
$\therefore$ Gain percentage $=\left(\frac{\text { gain }}{C P} \times 100\right) \%$
$=\left(\frac{195}{3250} \times 100\right) \%$
$=6 \%$
Hence, gain percent $=6 \%$