A shopkeeper marks his goods 30% above his cost price but allows a discount of 10% at the time of sale. His gain is

Question

A shopkeeper marks his goods 30% above his cost price but allows a discount of 10% at the time of sale. His gain is

1. A. 20%
2. B. 2.5%
3. C. 15%
4. D. 17% (Correct answer)

Correct Answer

Option D — 17%

Detailed Solution & Explanation

The correct answer is 17%.

Key Points

• Let the cost price be 100.
• Marked price is 30% above cost:
  • $MP = 100 \times 1.30 = 130$
• Selling price after a 10% discount on the marked price:
  • $SP = 130 \times 0.90 = 117$
• Gain:
  • $\text{Gain}\% = \frac{117 - 100}{100} \times 100 = \mathbf{17\%}$

Shortcut Trick

• Multiply the factors directly: $1.30 \times 0.90 = 1.17$, so the gain is 17%. Assuming $CP = 100$ makes the final figure *be* the percentage, which removes the last division step.

Alternate Method

• Use the successive change formula with $x = +30$ (markup) and $y = -10$ (discount):
  • $30 + (-10) + \frac{30 \times (-10)}{100} = 20 - 3 = 17\%$

Additional Information

• The trap in this question type is assuming the answer is $30\% - 10\% = 20\%$ (option A). It is not, because the discount is calculated on the marked price, which is larger than the cost price — so the 10% removed is worth more than 10% of the cost.
• General result: for a markup of $x\%$ followed by a discount of $y\%$,
  • $\text{Gain}\% = x - y - \frac{xy}{100}$
• Break-even check: the shopkeeper only loses money when $\frac{xy}{100} > x - y$, which for a 30% markup requires a discount above roughly 23%.