Question

A trader marks his goods 40% above the cost price and gives a discount of 20% on the marked price.Find his gain percent.

Answer 1

Given:-

•A trader marks his goods 40% above the cost price.

•He gives a discount of 20% on the marked price.

To Find:-

•Find his gain percent.

Solution:-

Let consider the cost price be x rupees and marked price be x+40%.

Then,

Using Formula:

$\: \: \sf \: marked \: price = (x + 40 percent \: of \: x \: rupees)$

Now substitute the values

$\: \: \sf \: marked \: price = rupees(x + \frac{40x}{100} ) \\ \\ \: \: \sf = rupees(x + \frac{2x}{5} ) \\ \\ \: \: \sf= rupees \frac{7x}{5}$

Hence,marked price is 7x/5 rupees.

Discount% = 20%

Now we have to use the formula of Selling Price

Using Formula:

$\: \: \sf \: sp = \frac{100 - discount percent}{100}$

Now substitute the values,

$\: \: \sf \: sp = ( \frac{100 - 20}{100} \times \frac{7x}{5} ) \\ \\ \: \: \sf = rupees \frac{28x}{25}$

Hence,Selling Price is 28x/25 rupees.

Now find profit

Using Formula:

$\: \: \sf \: profit = sp - cp$

Now substitute the values

$\: \: \sf \: profit = ( \frac{28x}{25} - x) \\ \\ \: \: \sf \: profit = \frac{3x}{25} rupees$

Hence,Profit is 3x/25rupees.

Now find Profit%

Using Formula:

$\: \: \sf \: profit percent = ( \frac{profit}{cp} \times 100)$

Now substitute the values

$\: \: \sf \: profit \: percent = ( \frac{3x}{25 \times x} \times 100) \\ \\ \: \: \sf \: profit \: percent = 12 \: percent$

Hence，profit percent is 12%.

Answer 2

Let the cost price be 100

Finding Marked price -

40% of 100 + 100

= 40 + 100

= 140

Marked Price = 140.  

Finding discount -

Discount on Marked Price.  

Discount % = 20 % (Given)

Discount = 140 x 20/100 = 28

Finding Selling Price -

Selling Price = Marked Price - Discount

Selling Price = 140 - 28

Selling Price = 112.

Finding  Gain -

Gain = Selling Price - Cost Price

Gain = 112 - 100

Gain = 12

Finding Gain Percentage -

Gain % = Gain/Cp x 100

Gain % = 12/100 x 100

Gain % = 12 %.

Hence :

Gain Percentage = 12%.