Question

a bookseller marks his book 40 % above the cost price and allows a discount of 25% find its gain or loss percent​

Answer 1

Let the cost price be 100
Then marked price = 100 + ( 100* 40/100)
= 140
Discount percent = 25%
Price after discount = 105
Profit percentage = 5/100 * 100
= 5%
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Answer 2

Given,

A book is marked 40% above the CP,

Discount allowed = 25%.

To find,

Gain or loss %.

Solution,

Firstly, let the cost price of the book be x.

Now, the bookseller marks it 40% above the CP, so the marked price of the book will be

$MP=x + \frac{40}{100} x$

$=\frac{140}{100} x$

Further, a discount of 25% is allowed by him, so the selling price will be

$SP=MP-\frac{25}{100} (MP)$

$=\frac{140}{100} x-\frac{25}{100} (\frac{140}{100} x)$

$=\frac{75}{100} (\frac{140}{100} x)$

Now, the gain or loss percent is given by

$Gain \%=\frac{SP-CP}{CP} \times 100$

$Loss \%=\frac{CP-SP}{CP} \times 100$

It can be seen that here, SP is coming out to be more than CP, so the bookseller makes a profit. So,

$Gain \%=\frac{\frac{75}{100} (\frac{140}{100} x)-x}{x} \times 100$

⇒ $Gain \%=({\frac{75}{100} (\frac{140}{100} )-1}) \times 100$

⇒ $Gain \%=({\frac{10500-10000}{100 \times 100}) \times 100$

⇒ $Gain \%=({\frac{500}{100 \times 100}) \times 100$

⇒ $Gain \%=5.$

Therefore, the bookseller makes a gain of 5%.