QUESTION 7 Direction: The question is followed by two statements (I) and (II).
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QUESTION 7
Direction: The question is followed by two statements (I) and (II). Answer the question using the following instructions:
Mark (A) if the question can be answered by one of the statements alone but not by the other
Mark (B) if the question can be answered by using either statement alone
Mark (C) if the question can be answered using both statements together, but cannot be answered using either statements alone
Mark (D) if the question cannot be answered
If Mohan gets a commission of 5% on selling price of a luxury car, then find the selling price of the car.
I. 25% of profit on sale of the car is Rs. 250000
II. SP is 25% higher than CP
Show answer & explanation
Statement I alone only gives us the profit amount (Rs. 250000 = 25% of profit, so total profit = Rs. 1000000), but without knowing CP or SP individually, we cannot find SP. Statement II alone tells us the relationship between SP and CP (SP = 1.25 × CP) but provides no numerical values to solve for SP. However, using both statements together: From I, Profit = Rs. 1000000. From II, SP = 1.25CP, so Profit = SP - CP = 1.25CP - CP = 0.25CP. Therefore, 0.25CP = 1000000, giving CP = Rs. 4000000 and SP = Rs. 5000000.
Step-by-step Derivation:
Step 1: Analyze Statement I alone
- Given: 25% of profit = Rs. 250000
- Therefore: Profit = Rs. 250000 × 4 = Rs. 1000000
- However, we need another relationship to find SP uniquely. Statement I alone is insufficient.
Step 2: Analyze Statement II alone
- Given: SP = 1.25 × CP
- This gives only a ratio, no numerical value. Statement II alone is insufficient.
Step 3: Combine both statements
- From Statement I: Profit = Rs. 1000000
- Profit = SP - CP
- From Statement II: SP = 1.25CP
- Substituting: 1000000 = 1.25CP - CP = 0.25CP
- Therefore: CP = 1000000 ÷ 0.25 = Rs. 4000000
- And: SP = 1.25 × 4000000 = Rs. 5000000
Step 4: Verification
- Profit = 5000000 - 4000000 = 1000000 ✓
- 25% of profit = 250000 ✓
- SP is 25% higher than CP: 5000000 = 1.25 × 4000000 ✓
Conclusion: Both statements together are necessary and sufficient to find SP = Rs. 5000000