Siddhart is a pen-seller. He sells a pen such that the profit earned b...
Let the profit be P and cost price be C.P
Then 10 P = C.P ....(I)
Selling Price = Cost Price + Profit = 10 P +P = 11P
Discount given = 3P.
Marked price = Selling Price + Discount = 11P+3P = 14P.
Let the discount given to ensure profit of 20% be d%.
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Siddhart is a pen-seller. He sells a pen such that the profit earned b...
Profit Calculation:
Let's assume the cost price of one pen is C.
According to the given information, the profit earned by selling 10 pens is equal to the cost price of 1 pen.
So, the profit earned by selling 10 pens = C
Discount Calculation:
Now, let's assume the marked price of one pen is M.
According to the given information, the discount offered by Siddhart is 3 times the profit earned by selling the pen.
So, the discount offered = 3 * C
Profit Percentage:
The profit percentage is given as 20%.
So, the profit earned by selling one pen = 20% of the cost price = 0.2C
Required Discount Percentage:
Let's assume the discount percentage offered by Siddhart is D%.
So, the selling price of one pen after discount = M - (D/100) * M
Profit earned by selling one pen after discount = Selling price - Cost price
= (M - (D/100) * M) - C
Given that, the profit earned by selling 10 pens is equal to the cost price of 1 pen.
So, the profit earned by selling 10 pens = 10 * (M - (D/100) * M) - C
According to the given information, the profit earned by selling 10 pens = C
So, 10 * (M - (D/100) * M) - C = C
Simplifying the equation,
10M - (10D/100)M - C = C
10M - (10D/100)M = 2C
10M - (D/10)M = 2C
(100 - D)M/10 = 2C
100 - D = 20C/M
D = 100 - (20C/M)
Substituting the value of C = profit earned by selling 10 pens,
D = 100 - (20 * C/M)
D = 100 - (20 * C)
Now, we need to find the approximate discount percentage that Siddhart should offer to have a profit of 20%.
Given that the discount offered = 3 * C
So, 3 * C = 100 - (20 * C)
23C = 100
C = 100/23
Substituting the value of C in the equation D = 100 - (20 * C),
D = 100 - (20 * (100/23))
D = 100 - (2000/23)
D = 100 - 86.9565
D ≈ 13.0435
Therefore, Siddhart should offer an approximate discount of 13.04% to have a profit of 20%.
Hence, the correct answer is option B) 14.28%.
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