Question

6. A cell phone was sold at a loss of 8%. It was observed that if the selling price
was 540 rupees more, the profit made would have been 10% what is the
actual selling price of the mobile?​

Answer 1

Let CP of Cell Phone=₹x

It was Sold at 8% loss

SP=CP-(CP×loss%)

$sp = x - (x \times 8\%) \\ \\ sp = x - (x \times \frac{8}{100} ) \\ \\ sp = x - \frac{2x}{25} \\ \\ = \frac{25x - 2x}{25} \\ \\ \frac{23x}{25} \\ \\ sp = \frac{23x}{25}$

Original SP=₹ 23x/25

If It was Sold at 540 more

Profit would be 10%

Now SP will be=23x/25+540

Means

If He sell at 23x/25+540 he would gain 10%

SP=CP+(CP×Gain%)

$x + (x \times 10\%) = \frac{23x}{25} + 540 \\ \\ x + (x \times \frac{10}{100} ) = \frac{23x}{25} + 540 \\ \\ x + \frac{x}{10} = \frac{23x}{25} + 540 \\ \\ \frac{10x + x}{10} = \frac{23x}{25} + 540 \\ \\ \frac{11x}{10} - \frac{23x}{25} = 540 \\ \\ \frac{11x \times 5 - 23x \times 2}{50} = 540 \\ \\ \frac{55x - 46x}{50} = 540 \\ \\ \frac{9x}{50} = 540 \\ \\ x = 540 \times \frac{50}{9} \\ \\ x = 60 \times 50 \\ \\ x = 3000$

CP=x=₹3000

Original SP=23x/25

$\frac{23 \times 3000}{25} \\ \\ 23 \times 120 \\ \\ = 2760$

Original SP=₹2760

SP=₹2760

Answer 2

Answer=₹2760

CP=>Cost price

SP=>Selling price

Cost price of Phone be x

Selling price =Cost price

Cost price ×loss%

$\begin{lgathered}selling\price =<strong> x - x</strong> \times 8\% \\ \\ selling\\: price = x - ((x \times \frac{8}{100})) \\ \\ selling\:price = x - \frac{2x}{25} \\ \\ = \frac{25x - 2x}{25} \\ \\ \frac{23x}{25} \\ \\ sp = \frac{23x}{25}\end{lgathered}$

$\begin{lgathered}x + x \times 10\% = \frac{23x}{25} + 540 \\ \\ x + x \times \frac{10}{100} = \frac{23x}{25} + 540 \\ \\ x + \frac{x}{10} = \frac{23x}{25} + 540 \\ \\ \frac{10x + x}{10} = \frac{23x}{25} + 540 \\ \\ \frac{11x}{10} - \frac{23x}{25} = 540 \\ \\ \frac{11x \times 5 - 23x \times 2}{50} = 540 \\ \\ \frac{55x - 46x}{50} = 540 \\ \\ \frac{9x}{50} = 540 \\ \\ x = 540 \times \frac{50}{9} \\ \\ x = 60 \times 50 \\ \\ x = 3000\end{lgathered}$

$\begin{lgathered}\frac{23 \times 3000}{25} \\ \\ 23 \times 120 \\ \\ answer= 2760\end{lgathered}$

Actual Selling price of the mobile =₹2760