Final answer:
The overall percentage when Sanjith sold one bike at a 10% loss and another at a 20% profit, both at the same price, is calculated using the weighted average of the percentages, taking into account the different cost prices. The correct calculation reveals that the overall percentage is 2.857%. Therefore, the correct option is d.
Step-by-step explanation:
The student's question pertains to percentage problems related to profit and loss in Mathematics. To solve the question, we need to understand that Sanjith sold two bikes at the same price, one at a 10% loss and the other at a 20% profit. To determine his overall percentage, we need to calculate the average of the two percentages.
However, since the question is mentioned with various options such as a. 2.425 b. 1.687 c. 2.525 d. 2.857, and none of these options match the reference information provided, we would not use those references. Instead, we will assume that both bikes were sold for the same price which we will denote as P for each bike. Consider the cost price of the first bike to be C1 and the second bike C2.
For the first bike:
Loss = 10% of C1
Selling Price of bike 1 (SP1) = C1 - (10/100)*C1 = 0.9*C1
For the second bike:
Profit = 20% of C2
Selling Price of bike 2 (SP2) = C2 + (20/100)*C2 = 1.2*C2
Since SP1 = SP2 = P (The bikes were sold at the same price), we have:
0.9*C1 = 1.2*C2
C1/C2 = 1.2/0.9
C1/C2 = 4/3
To find out the net effect, we take an average of the two percentages based on the cost prices of bikes. As we know, average percentage change doesn’t work simply on averaging out the two percentages, because the cost prices are different. We need to take a weighted average.
The overall percentage gain or loss can be expressed as:
Total percentage = [(C1*(-10%) + C2*(20%)) / (C1 + C2)]*100
Substituting the ratio we have for C1/C2 into the equation, we get:
Total percentage = [(4*(-10) + 3*(20)) / (4 + 3)]
Total percentage = (-40 + 60) / 7
Total percentage = 20/7
Total percentage = 2.857%
The correct option in the final part of the student's question is d. 2.857.