Question

A radio which a dealer bought for $60,000 and marked to give a profit of 30% was reduced in sale by 10%. Find the final selling price and the percentage profit.

Answer 1

Let:

Op = Original price

Pp = Price to get a profit of 30%

Fp = Final price

So:

`\begin{gathered} Pp=Op+0.3\cdot Op \\ Pp=60000+0.3\cdot60000 \\ Pp=60000+18000 \\ Pp=78000 \end{gathered}`
`\begin{gathered} Fp=Pp-0.1\cdot Pp \\ Fp=78000-0.1\cdot78000 \\ Fp=78000-7800 \\ Fp=70200 \end{gathered}`

The final price is $70200 and the percentage profit is:

`\begin{gathered} 70200=60000+r\cdot60000 \\ 60000r=70200-60000 \\ 60000r=10200 \\ r=(10200)/(60000) \\ r=0.17 \end{gathered}`

The percentage profit of the final price is 17%