A dealer sells a product at 15% profit. If he had bought it at 10% less and sold it for ₹126 less, he would have gained 20%. Find…

Question

A dealer sells a product at 15% profit. If he had bought it at 10% less and sold it for ₹126 less, he would have gained 20%. Find the cost price.

1. A. ₹1,400
2. B. ₹1,800 (Correct answer)
3. C. ₹2,000
4. D. ₹1,200

Correct Answer

Option B — ₹1,800

Detailed Solution & Explanation

The correct answer is ₹1,800.

Shortcut Trick

• Work in units instead of rupees and the arithmetic collapses to one division.
• Assume the original CP = 100 units. Then the original SP = 115 units (15% profit).
• New CP is 10% less, so CP₂ = 90 units. A 20% gain on that gives SP₂ = 90 × 1.20 = 108 units.
• Difference in selling price = 115 − 108 = 7 units, and the question tells us that difference is ₹126.
• So 7 units = ₹126 → 1 unit = ₹18, and the original CP of 100 units = ₹1,800.

Alternate Method

• Let the cost price be ₹x.
  • Original selling price: $SP_1 = 1.15x$
  • Reduced cost price: $CP_2 = 0.90x$
  • New selling price at 20% gain: $SP_2 = 0.90x \times 1.20 = 1.08x$
• Given $SP_1 - SP_2 = 126$:
  • $1.15x - 1.08x = 126$
  • $0.07x = 126$
  • $x = 126 \div 0.07 = \textbf{1800}$

Additional Information

• Profit % $= \dfrac{\text{Profit}}{CP} \times 100$, and $SP = CP \times \dfrac{100 + \text{Profit\%}}{100}$.
• Successive percentage change: a change of $a\%$ followed by $b\%$ gives a net change of $\left(a + b + \dfrac{ab}{100}\right)\%$. Here a 10% fall in CP with a 20% gain nets $-10 + 20 - 2 = +8\%$, which is why $SP_2 = 1.08x$ directly.
• The unit method works whenever the question gives only percentages plus one absolute figure — assume 100, compute the difference in units, then scale.