Question

A radio was sold for rupee 3120 at a loss of 4% what will the gain or loss per cent if it is sold for 3445

Answer 1

Ok

Let The Original Price Be x

Now On Selling It At 3120 Is 4% Loss

So

x-4/100*x = 3120

24x/25 = 3120

x = 3120*25/24 = 3250

So Original Price Is 3250

Now

Profit Would Be There As 3445> 3250

So Profit = Profit/Original Price * 100

3445-3250/3250 * 100

=> 195/3250 * 100

=> 0.06*100

=> 6

So There Is Gain Of 6%

Answer 2

Given :-

Selling price of radio at loss of 4% is Rs.3120

To Find :-

Gain or loss% when the selling price of the radio is Rs.3445.

Solution :-

We have ,

Loss% = 4%

Selling price (SP) = Rs.3120

Cost price (CP) = ?

$\begin{gathered} \\ \star \: {\boxed{\sf{\purple{ SP= (1 - \frac{loss\%}{100}) \times CP }}}} \\ \end{gathered}$

Substituting the values we have ,

$\begin{gathered} \\ : \implies \sf \: 3120 =(1 - \frac{4 }{100}) \times CP \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: 3120 = \frac{100 - 4}{100} \times \: CP \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: 3120 = \frac{96}{100} \times CP \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: CP = 3120 \: \times \: \frac{100}{96} \\ \\ \end{gathered}$

$\begin{gathered} \\ \implies \sf \purple{ \: ∵ CP = Rs.3250} \\ \\ \end{gathered}$

Since the change in Cost price is not mentioned . The Cost price will remain constant i.e , Rs.3250.

Selling price = Rs.3445 [Given]

Here (SP) > (CP)

So , There must be a profit.

$\begin{gathered} \\ : \implies \sf \: Profit \: =SP - CP \\ \\ \end{gathered}$

$\implies \sf {profit \: = \: 3445 - 3250} \\ \\ \implies \sf{profit \: = \: 195}$

Profit% of an article is given by ,

$\implies\sf \purple{profit\% \: = \: ( \frac{profit}{CP} \times 100)\% }$

Substituting the values ,

$\begin{gathered} \\ : \implies \sf \: profit\% = \frac{195}{3250} \times 100\%\\ \\ \end{gathered} </p><p>$

$\implies \sf \purple{profit\% \: = \: 6\% \: \: \: (ans)}$

hope it helps you....