Lesle sold her tow bikes, one at 10% loss and the other at 20% profit. Find her overall profit percentage if she sold both the bikes at the same price.
A. 2.857%
B. 2.625%
C. 2.425%
D. 1.687%
Answers
To find:
Overall profit percentage if she sold both the bikes at the same price
Step-by-step explanation:
Let the selling price of each bike is x
The first bike was sold at 10% loss.
Then its cost price
= x/(1 - 10/100)
= x/(90/100)
= 100x/90
= 10x/9
The second price was sold at 20% profit.
Then its cost price
= x/(1 + 20/100)
= x/(120/100)
= 100x/120
= 5x/6
Since it is mentioned that the selling was a profit, then profit
= (x + x) - (10x/9 + 5x/6)
= 2x - (20x + 15x)/18
= 2x - 35x/18
= (36x - 35x)/18
= x/18
Total cost price of the two bikes
= 10x/9 + 5x/6
= 35x/18
Hence profit percentage
= total profit / total cost price * 100 %
= (x/18) / (35x/18) * 100 %
= 1/35 * 100 %
= 2.857 %
Final answer: A. 2.857%
Her overall profit percentage be 2.857% if she sold both the bikes at the same price.
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Given:
Total num er of bikes = 2
Loss at which bike is sold = 10%
Profit at which bike is sold = 20%
To Find:
Overall profit percentage if both the bikes were sold at the same price.
Solution:
Let the CP of first bike be = 100x
Let the CP of second bike = 100y
Therefore,
CP = 100x + 100y
Sold at 10 % loss
= 10/100 x 100x
= 10x
Thus, SP = 100x - 10x
= 90x
Sold at 20 % profit
= 20/100 x 100y
= 20y
SP = 100y + 20y
= 120y
Now 90x = 120y
Total SP = 90x + 120y = 180x
Now,
CP = 100x + 100y
Substituting value -
= 100x + 100(3x/4)
= 175x
Profit = 180x - 175x
= 5x
Profit %
= 5x/175x x 100
= 2.857 %
Answer: The overall profit is A. 2.857%