SSC CGL Exam > SSC CGL Questions > P calculates his profit percent on selling pr...
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P calculates his profit percent on selling price while Q calculates his profit percent on cost price. They notice that difference between their profits is 1000 rupees. If selling price of both P and Q are same and P gets 40% profit and Q gets 60% profit. Then find their selling price
- a)77500
- b)40000
- c)97500
- d)10500
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
P calculates his profit percent on selling price while Q calculates hi...
Given:
- Profit Calculation Methods:
- P calculates profit on Selling Price (SP).
- Q calculates profit on Cost Price (CP).
- Profits:
- P's profit: 40% of SP.
- Q's profit: 60% of CP.
- Difference in Profits: ₹1,000.
- Selling Price for both P and Q: Same and denoted as S.
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Steps to Calculate the Selling Price
- Calculate P's Cost Price (CPP):
- P's profit is 40% of SP.
- ProfitP = 0.40 x S
- CPP = SP - ProfitP = S - 0.40S = 0.60S
- Calculate Q's Cost Price (CPQ):
- Q's profit is 60% of CPQ.
- ProfitQ = 0.60 x CPQ
- Selling Price for Q: SP = CPQ + ProfitQ = CPQ + 0.60CPQ = 1.60CPQ
- Therefore, CPQ = SP / 1.60 = S / 1.60
- ProfitQ = 0.60 x (S / 1.60) = 0.375S
- Set Up the Profit Difference Equation:
- Difference in profits: ProfitP - ProfitQ = ₹1,000
- Substitute the expressions for profits:
- 0.40S - 0.375S = 1,000
- 0.025S = 1,000
- S = 1,000 / 0.025 = 40,000
- Conclusion:
- The selling price for both P and Q is ₹40,000.
Final Answer
The selling price for both P and Q is ₹40,000.
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Community Answer
P calculates his profit percent on selling price while Q calculates hi...
Understanding the Problem
P and Q have the same selling price (SP) but calculate their profit percentages differently. P calculates profit based on SP, while Q calculates profit based on cost price (CP). The difference in their profits is 1000 rupees.
Key Information
- P's profit percentage = 40%
- Q's profit percentage = 60%
- Difference in profits = 1000 rupees
Calculating Profit for P and Q
- Let SP = S
- For P:
- Profit = 40% of S = 0.4S
- Thus, CP of P = SP - Profit = S - 0.4S = 0.6S
- For Q:
- Profit = 60% of CP of Q
- Let CP of Q = C, then Profit = 0.6C
- Since both have the same SP, we have:
- S = C + 0.6C = 1.6C
- Therefore, C = S / 1.6
Setting Up the Equation
Since the difference in profits is 1000 rupees, we can set up the equation:
0.4S - 0.6C = 1000
Substituting C:
0.4S - 0.6(S / 1.6) = 1000
Simplifying the Equation
Multiply 0.6(S / 1.6) by 1.6 to eliminate the fraction:
0.4S - 0.375S = 1000
This simplifies to:
0.025S = 1000
Finding the Selling Price
Now, solving for S:
S = 1000 / 0.025 = 40000
Thus, the selling price for both P and Q is:
Final Answer
Selling Price = 40000 rupees (Option B)
P and Q have the same selling price (SP) but calculate their profit percentages differently. P calculates profit based on SP, while Q calculates profit based on cost price (CP). The difference in their profits is 1000 rupees.
Key Information
- P's profit percentage = 40%
- Q's profit percentage = 60%
- Difference in profits = 1000 rupees
Calculating Profit for P and Q
- Let SP = S
- For P:
- Profit = 40% of S = 0.4S
- Thus, CP of P = SP - Profit = S - 0.4S = 0.6S
- For Q:
- Profit = 60% of CP of Q
- Let CP of Q = C, then Profit = 0.6C
- Since both have the same SP, we have:
- S = C + 0.6C = 1.6C
- Therefore, C = S / 1.6
Setting Up the Equation
Since the difference in profits is 1000 rupees, we can set up the equation:
0.4S - 0.6C = 1000
Substituting C:
0.4S - 0.6(S / 1.6) = 1000
Simplifying the Equation
Multiply 0.6(S / 1.6) by 1.6 to eliminate the fraction:
0.4S - 0.375S = 1000
This simplifies to:
0.025S = 1000
Finding the Selling Price
Now, solving for S:
S = 1000 / 0.025 = 40000
Thus, the selling price for both P and Q is:
Final Answer
Selling Price = 40000 rupees (Option B)
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