DIRECTIONS: In the following questions the first word is related to th...
Let C.P. = Rs. x, S.P. = Rs. y
Profit = y - x
According to question
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DIRECTIONS: In the following questions the first word is related to th...
Understanding the Problem
The problem states that when the selling price (SP) is doubled, the profit (P) triples. To determine the profit percentage, we need to establish the relationship between cost price (CP), selling price, and profit.
Definitions
- Cost Price (CP): The original price of the item.
- Selling Price (SP): The price at which the item is sold.
- Profit (P): The difference between selling price and cost price, calculated as P = SP - CP.
Setting Up the Relationship
1. Let the initial selling price be SP = x.
2. The profit when selling at this price is given by P = x - CP.
3. When the selling price is doubled, we have SP = 2x.
4. The new profit becomes P' = 2x - CP.
According to the problem, the new profit is three times the original profit:
Equation Formulation
- P' = 3P
- Therefore, 2x - CP = 3(x - CP).
Solving the Equation
1. Expanding the equation:
- 2x - CP = 3x - 3CP
2. Rearranging gives:
- 2x + 2CP = 3x
- This simplifies to CP = x.
Calculating Profit Percentage
Now that we know CP = x, we can calculate the profit percentage:
- Profit, P = SP - CP = x - x = 0 (initially).
- When SP is doubled, P = 2x - x = x.
- Profit percentage formula is: (Profit/CP) × 100.
Since CP = x, the profit percentage becomes:
- (x/x) × 100 = 100%.
Conclusion
Thus, the profit percentage is 100%, making the correct answer option 'B'.