Question

9
On selling a product, a dealer gained 20%. If he had sold for Rs. 150 less, he would have lost 10%. What is the cost price of
the product?​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Cost\:price=500\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Profit\% = 20\% \\ \\ \tt: \implies S.P - 150 = 10\% \: loss \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Cost \: Price = ?$

• According to given question :

$\text{let \:C.P \: be \: x} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies S.P = x + 20\% \: of \: x \\ \\ \tt: \implies S.P= x + 0.2x \\ \\ \tt: \implies S.P =1.2x \\ \\ \bold{As \: according \: to \: given \: condition} \\ \tt: \implies S.P - 150 = x - 10\% \: of \: x \\ \\ \tt: \implies 1.2x - 150 = x - 0.1x \\ \\ \tt: \implies 1.2x - 150 = 0.9x \\ \\ \tt: \implies 1.2x - 0.9x = 150 \\ \\ \tt: \implies 0.3x = 150 \\ \\ \tt: \implies x = \frac{150}{0.3} \\ \\ \green{ \tt: \implies x = 500 \: rupees} \\ \\ \green{\tt \therefore Cost \: Price \: of \: product \: is \: 500}$

Answer 2

Given:-

$\sf Profit\%= 20\%\\ \\ \sf\bullet S.P-150= 10\% loss$

To find

The C.P of product

A.T.Q:-

let the C.P be n

• Then we know that
• S .P =C.P +Profit

$\sf\implies S.P= n+ 20\% of n\\ \\ \sf\implies S.P=n+\cancel{\dfrac{20n}{100}}\\ \\ \sf\implies S.P= n+\dfrac{n}{5}\\ \\ \sf\implies S.P= \dfrac{6n}{5}$

Now

$\sf\implies \dfrac{6n}{5}-150= n-10\%of\:n\\ \\ \sf\implies \dfrac{6n-7500}{5}= n-\cancel{\dfrac{10n}{100}}\\ \\ \sf\implies \dfrac{6n-750}{5}= \dfrac{10n-n}{10}\\ \\ \sf\implies \dfrac{6n-750}{5}=\dfrac{9n}{10}\\ \\ \sf\:\:\:Now\:cross\: multiplication\\ \\ \sf\implies 10(6n-750)= 5\times 9n\\ \\ \sf\implies 60n-7500= 45n\\ \\ \sf\implies 60n=45n+7500\\ \\ \sf\implies 60n-45n=7500\\ \\ \sf\implies 15n=7500\\ \\ \sf\implies n=\cancel{\dfrac{7500}{15}}\\ \\ \sf\implies n=500$

$\boxed{\sf{Cost \: price=500\:rupee}}$