Question

If a person buys 15 pencils for ₹12, and sells 12 pencils for ₹15, find the gain or loss percentage.

• A. Loss of 56.25%
• B. Gain of 65.25%
• C. Loss of 56.52%
• D. Gain of 56.25%

Hint:

To solve this faster, use the cross-multiplication method: $(15 \times 15) - (12 \times 12) = 225 - 144 = 81$. Then Gain % = $(81 / 144) \times 100 = 56.25\%$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To calculate gain or loss percentage, the number of items bought and sold must be made equal, or we must find the cost and selling price of a single unit. If the selling price is higher than the cost price, it is a gain.

Step 2: Key Formula or Approach:
We will find the Cost Price (CP) and Selling Price (SP) for 1 pencil. \[ \text{Gain \%} = \left( \frac{SP - CP}{CP} \right) \times 100 \]

Step 3: Detailed Explanation:
Given: Cost Price of 15 pencils = ₹12 \[ CP \text{ of 1 pencil} = \frac{12}{15} = ₹0.8 \] Selling Price of 12 pencils = ₹15 \[ SP \text{ of 1 pencil} = \frac{15}{12} = ₹1.25 \] Since $SP > CP$, there is a gain: \[ \text{Gain} = 1.25 - 0.8 = ₹0.45 \] \[ \text{Gain \%} = \left( \frac{0.45}{0.8} \right) \times 100 \] \[ \text{Gain \%} = \frac{45}{80} \times 100 = \frac{9}{16} \times 100 = 56.25\% \]

Step 4: Final Answer:
The person has a gain of 56.25%.