Question

A radio is sold for Rs. 1230 at a loss of 18%. What would have been gained or loss per cent if it had been sold for Rs. 1600 ?​

Answer 1

Answer:

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Answer 2

Given :-

Selling price of radio at loss of 18% is Rs.1230

To Find :-

Gain or loss% when the selling price of the radio is Rs.1600

Solution :-

We have ,

Loss% = 18%

Selling price (SP) = Rs.1230

Cost price (CP) = ?

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

Substituting the values we have ,

$\begin{gathered} \\ : \implies \sf \: 1230 =(1 - \frac{18 }{100}) \times CP \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: 1230 = \frac{100 - 18}{100} \times \: CP \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: 1230 = \frac{82}{100} \times CP \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: CP = 1230 \: \times \: \frac{100}{82} \\ \\ \end{gathered}$

$\begin{gathered} \\ \implies \sf \purple{ \: ∵ CP = Rs.1500} \\ \\ \end{gathered}$

Since the change in Cost price is not mentioned . The Cost price will remain constant i.e , Rs.1500.

Selling price = Rs.1600 [Given]

Here (SP) > (CP)

So , There must be a profit.

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

$\implies \sf {profit \: = \: 1600 - 1500} \\ \\ \implies \sf{profit \: = \: 100}$

Profit% of an article is given by ,

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

Substituting the values ,

$\begin{gathered} \\ : \implies \sf \: profit\% = \frac{100}{1500} \times 100\%\\ \\ \end{gathered} </p><p>$

$\implies \sf{profit\% \: = \: \frac{20}{3}\% }$

$\implies \sf \purple{profit\% \: = \: 2 \frac{6}{3} \% \: \: \: (ans)}$

hope it helps you....