Question

a shop keeper marks his goods 30% above the cost price and allow a discount 15% on them. then what percentage does he gains.

Answer 1

Let the CP of an item be x...
So, MP = 30% above CP.....
$= x + (30\% \: of \: x) \\ = x + \frac{30}{100} x \\ = \frac{130}{100} x$
Now, Discount = 15%.....
$= 15\% \: of \: mp \\ = \frac{15}{100} \times \frac{130}{100} x \\ = \frac{195}{1000} x$
So, SP = MP - DISCOUNT
$= \frac{130}{100} x - \frac{195}{1000} x \\ = \frac{(1300 - 195)}{1000} x \\ = \frac{1105}{1000} x \\ = 1.105x$
Now.....Since SP > CP.....
THEREFORE,
Profit = 1.105x - x = 0.105x
And Hence,
Profit % =
$\frac{profit}{cp} \times 100 \\ = \frac{0.105x}{x} \times 100 \\ = 0.105 \times 100 \\ = 10.5\%$
THEREFORE HE GETS A GAIN OF 10.5%.....

*****ALTERNATIVE*****

Let the CP of an item be 100.....
MP = 30% above CP
$= 100 + 30\% \: of \: 100 \\ = 100 + \frac{30}{100 } \times 100 \\ = 100 + 30 \\ = 130$
Now, Discount = 15%.....
$15\% \: of \: mp \\ = \frac{15}{100} \times 130 \\ = \frac{195}{10}$
So, SP = MP - DISCOUNT
$= 130 - \frac{195}{10} \\ = \frac{(1300 - 195)}{10} \\ = \frac{1105}{10} \\ = 110.5$
Now.....SINCE.....SP > CP.....
THEREFORE,
Profit = SP - CP
$= 110.5 - 100 \\ = 10.5$
And HENCE,
Profit % =
$\frac{profit}{cp} \times 100 \\ = \frac{10.5}{100} \times 100 \\ = 10.5\%$
THEREFORE HE GETS A GAIN OF 10.5%.....

THERE YOU GO!!!.....