An item is sold at a price that gives a 40% profit. If its cost had been 40% lower and it had been sold for Rs 5 less than the original selling price, the profit would have been 50%. Find the original selling price.
Answer and solution
Correct answer: B
Solution
Answer: B — Rs 14
1. Let original cost be C. At 40% profit the original selling price is 1.4C.
2. The reduced cost would be 0.6C. At 50% profit its selling price would be 1.5×0.6C=0.9C.
3. This hypothetical price is ₹5 below the original: 1.4C−0.9C=5. Hence C=10.
4. Original selling price=1.4×10=₹14, option B. Check new cost ₹6 and new SP ₹9 give 50% profit.
Why this method works:
Both profit percentages use their own cost prices. In the hypothetical case the cost is 60% of the original, so 50% profit makes the hypothetical selling price 90% of the original cost. It is not 50% above the original cost.
Independent check and common trap:
Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.
Apply: Old SP=140% of original CP. New SP=150% of 60%=90% of original CP. The 50% gap is ₹5, so CP=₹10 and SP=₹14.
Check: Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.
1. Let original cost be C. At 40% profit the original selling price is 1.4C.
2. The reduced cost would be 0.6C. At 50% profit its selling price would be 1.5×0.6C=0.9C.
3. This hypothetical price is ₹5 below the original: 1.4C−0.9C=5. Hence C=10.
4. Original selling price=1.4×10=₹14, option B. Check new cost ₹6 and new SP ₹9 give 50% profit.
Why this method works:
Both profit percentages use their own cost prices. In the hypothetical case the cost is 60% of the original, so 50% profit makes the hypothetical selling price 90% of the original cost. It is not 50% above the original cost.
Independent check and common trap:
Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.
G Strategy shortcut
Spot: Profit and Loss.Apply: Old SP=140% of original CP. New SP=150% of 60%=90% of original CP. The 50% gap is ₹5, so CP=₹10 and SP=₹14.
Check: Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.
G Strategy: Spot: Profit and Loss. Apply: Old SP=140% of original CP. New SP=150% of 60%=90% of original CP. The 50% gap is ₹5, so CP=₹10 and SP=₹14. Check: Original cost₹10 gives selling price₹14. The alternative cost₹6 gives selling price₹9, earning₹3 or 50% profit. The two selling prices differ by₹5, as required; the requested answer is₹14 rather than cost₹10.