By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

Question

By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

1. A. 2700 (Correct answer)
2. B. 2750
3. C. 20750
4. D. 27000

Correct Answer

Option A — 2700

Detailed Solution & Explanation

The correct answer is 2700.

Key Points

• Step 1 — find the cost price from the 14% gain:
  • $SP = CP \times \left(1 + \frac{\text{gain}\%}{100}\right)$
  • $2850 = CP \times 1.14$
  • $CP = \frac{2850}{1.14} = 2500$
• Step 2 — compute the new selling price at 8% profit:
  • $SP' = 2500 \times 1.08 = \mathbf{2700}$

Shortcut Trick

• Work with the ratio of the two multiplying factors and skip the cost price entirely:
  • $SP' = 2850 \times \frac{1.08}{1.14} = 2850 \times \frac{108}{114} = 2850 \times \frac{18}{19} = 2700$
• The fraction $\frac{108}{114}$ reduces to $\frac{18}{19}$, and $2850 \div 19 = 150$, so $150 \times 18 = 2700$ in one line.

Alternate Method

• Since $CP = 2500$, each 1% of cost price is Rs. 25. A 14% gain is Rs. 350 (giving 2850 ✓) and an 8% gain is Rs. 200, so $SP' = 2500 + 200 = 2700$.

Additional Information

• The core relationships:
  • $\text{Gain}\% = \frac{SP - CP}{CP} \times 100$
  • $\text{Loss}\% = \frac{CP - SP}{CP} \times 100$
• Profit and loss percentages are always calculated on the cost price, never on the selling price, unless the question explicitly says otherwise.
• Distractor check: options 20,750 and 27,000 are decimal-shift traps — a quick order-of-magnitude glance rules them out, since the new price must be slightly *below* 2,850.