Question

21) If the profit percentage earned by selling a radio is 28% , then find the ratio of the cost price to the selling price of the radio.

Answer 1

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

$\green{\tt{\therefore{Ratio=25:32}}}$

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

$\green {\underline \bold{Given :}} \\ \tt: \implies Profit \% = 28\% \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Ratio \: of \: Cost \: price \:and \: Selling \: price = ?$

• According to given question :

$\circ\:\text{let \: c.p \: be \: x} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Selling \: price = x + 28\% \: of \: x \\ \\ \tt: \implies Selling \: price =x + \frac{28}{100} \times x \\ \\ \tt: \implies Selling \: price =x + 0.28x \\ \\ \green{\tt: \implies Selling \: price =1.28x} \\ \\ \bold{For \: Ratio:} \\ \tt: \implies Ratio = \frac{Cost \: price}{Selling \: price} \\ \\ \tt: \implies Ratio = \frac{x}{1.28x} \\ \\ \tt: \implies Ratio = \frac{1}{1.28} \\ \\ \tt: \implies Ratio = \frac{100}{128} \\ \\ \tt: \implies Ratio = \frac{25}{32} \\ \\ \green{\tt: \implies Ratio =25 : 32}$

Answer 2

Given:-

Profit %= 28%

To find

The ratio of C.P and S.P

Now A.T.Q

let the C.P of radio be y

we know that

$\sf\implies S.P =C.P +Profit\\ \\ \sf\implies S.P = y+\dfrac{28}{100}y\\ \\ \sf\implies S.P= y+0.28y\\ \\ \sf\implies S.P = 1.28y$

Now the ratio

$\sf\implies ratio=\dfrac{C.P}{S.P}\\ \\ \sf\implies Ratio=\dfrac{y}{1.28y}\times \dfrac{100}{100}\\ \\ \sf\implies ratio=\dfrac{100y}{128}\\ \\ \sf\implies ratio= \dfrac{\cancel{100y}}{\cancel{128y}}\\ \\ \sf\implies ratio= \dfrac{25}{32}\\ \\ \sf{\purple{ratio=25:32}}$

$\boxed{\sf{ratio=25:32}}$