If the selling price of 12 books is equivalent to the cost price of 18 copies, then calculate the profit percent.

Question

If the selling price of 12 books is equivalent to the cost price of 18 copies, then calculate the profit percent.

1. A. 44%
2. B. 50% (Correct answer)
3. C. 55%
4. D. 25%

Correct Answer

Option B — 50%

Detailed Solution & Explanation

The correct answer is 50%.

Key Points

• Given: SP of 12 books = CP of 18 books.
• Let the cost price of one book be Rs. 1, so the cost price of 18 books is Rs. 18.
• That Rs. 18 is the money received for selling 12 books, so:
  • $SP \text{ of } 12 \text{ books} = 18, \qquad CP \text{ of } 12 \text{ books} = 12$
• Profit percentage:
  • $\frac{18 - 12}{12} \times 100 = \frac{6}{12} \times 100 = \mathbf{50\%}$

Shortcut Trick

• When the selling price of $a$ articles equals the cost price of $b$ articles:
  • $\text{Profit}\% = \frac{b - a}{a} \times 100$
• Here $a = 12$, $b = 18$: $\frac{18 - 12}{12} \times 100 = 50\%$.
• Sign rule: if $b > a$ it is a profit; if $b < a$ it is a loss.

Additional Information

• The intuition: the trader receives the money for 18 books while parting with only 12. The extra 6 books' worth of revenue, measured against the 12 books actually given up, is the gain — hence $\frac{6}{12} = 50\%$.
• Worth memorising: SP of 10 = CP of 12 → 20% profit; SP of 8 = CP of 10 → 25% profit; SP of 15 = CP of 12 → 20% loss.
• Distractor check: 44% comes from computing $\frac{18-12}{18}$ — dividing by the wrong base. Profit percentage is always measured on the cost price.