# Question #e3826

Dec 20, 2017

The dealer must mark the computer 30% above the cost price.

#### Explanation:

The dealer needs to give a discount of 5%,

$\therefore$ Selling price (SP) = Marked price(MP) - Discount:

$\implies S P = M P - \frac{5}{100} \times M P$......... ($\because$ discount is 5%)

$\implies S P = M P \left(1 - 0.05\right) = 0.95 \times M P$

$\implies S P = 0.95 \times M P$..... equation(1)

He wants a profit of 23.5 % on the Cost price (CP):

So he needs to sell it for :

$S P = C P + \frac{23.5}{100} \times C P$

$\implies S P = C P \left(1 + 0.235\right)$

$\implies S P = 1.235 \times C P$ ........ equation (2)

Equating (1) and (2):

$1.235 \times C P = 0.95 \times M P$

$\implies M P = \frac{1.235}{0.95} \times C P$

$\implies M P = 1.3 \times C P$

$\implies M P = C P \left(1 + 0.3\right)$

$\implies M P = C P + \frac{30}{100} \times C P$

So the dealer must mark the computer 30% above the cost price.

$\underline{C r o s s - c h e c k}$:

Let CP = 100
MP will be 130

After giving Discount 5% ,
$S P = 130 - \frac{5}{100} \times 130 = 130 - 6.5$

$\therefore S P = 123.5$ where CP was 100.

So he gets 23.5 % profit.