Answer:
[tex] \boxed{ \boxed{ \sf {Marked \: price \: = Rs \: 1500}}}[/tex]
[tex] \boxed{ \bold{ \boxed{ \sf{Selling \: price = \: Rs \: 1230}}}}[/tex]
Step-by-step explanation:
Let Cost price ( C.P ) be x
Finding the Marked price and selling price
Marked price = [tex] \sf{x + 20\% \: of \: x}[/tex]
⇒[tex] \sf{x + \frac{20}{100} \times x}[/tex]
⇒[tex] \sf{ \frac{x \times 100 + 20x}{100} }[/tex]
⇒[tex] \sf{ \frac{120x}{100} }[/tex] ⇒ ( i )
Selling price = [tex] \sf{marked \: price \: - 18\% \: of \: marked \: price}[/tex]
⇒[tex] \sf{ \frac{120x}{100} - \frac{18}{100} \times \frac{120x}{100} }[/tex]
⇒[tex] \sf{ \frac{120x}{100} - \frac{54x}{250} }[/tex]
⇒[tex] \sf{ \frac{120x \times 5 - 54x \times 2}{500} }[/tex]
⇒[tex] \sf{ \frac{600x - 108x}{500} }[/tex]
⇒[tex] \sf{ \frac{492x}{500} }[/tex] ⇒ ( ii )
Finding the value of x ( Cost price )
[tex] \sf{loss = cost \: price - selling \: price}[/tex]
⇒[tex] \sf{20 = x - \frac{492x}{500} }[/tex]
⇒[tex] \sf{20 = \frac{x \times 500 - 492x}{500} }[/tex]
⇒[tex] \sf{20 = \frac{8x}{500} }[/tex]
⇒[tex] \sf{8x = 10000}[/tex]
⇒[tex] \sf{x = \frac{10000}{8} }[/tex]
⇒[tex] \sf{x = \: Rs \: 1250}[/tex]
Value of x ( cost price ) = Rs 1250
Now, Replacing the value of x in ( i ) in order to find the value of marked price
[tex] \sf{marked \: price = \frac{120x}{100} }[/tex]
⇒[tex] \sf{ \frac{120 \times 1250}{100} }[/tex]
⇒[tex] \sf{ \: Rs \: 1500}[/tex]
Replacing value of x in ( ii ) in order to find the value of selling price
[tex] \sf{selling \: price = \frac{492 \: x}{500} }[/tex]
⇒[tex] \sf{ \frac{615000}{500} }[/tex]
⇒[tex] \sf{ \: Rs \: 1230}[/tex]
Thus , Marked price of the fan = Rs 1500
Selling price of the fan = Rs 1230
Hope I helped!
Best regards!!
