CAT 2023

Slot 3

QA

Question & Solution

1. Concept Used

• Topic: Profit and Loss with Dishonest Dealings (False Measure + Bonus Stock + Discount)
• Formula: $$\text{Profit %} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100$$

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2. Calculation

Let us anchor the entire problem to a fixed quantity of cloth: 105 cm, which is the effective unit the merchant works with on the buying side.

Step 1 — Cost Price Analysis (Buying Side):

The merchant pays Rs. 100 for every 100 cm but receives 5 cm free. So effectively: $$\text{Cost Price of 105 cm} = \text{Rs. } 100$$

Step 2 — Selling Price Analysis (Selling Side):

The merchant's Marked Price is Rs. 110 per 100 cm. However, he cheats by giving only 95 cm when the customer pays for 100 cm. This means: $$\text{He charges for 100 cm but delivers only 95 cm}$$

So, the Marked Price for 95 cm of cloth = Rs. 110.

After a 5% discount, the Selling Price for 95 cm becomes: $$\text{SP for 95 cm} = 110 \times \left(1 - \frac{5}{100}\right) = 110 \times \frac{19}{20} = \text{Rs. } 104.5$$

Step 3 — Scale SP to 105 cm:

Now we need the Selling Price for 105 cm (to compare with CP of 105 cm = Rs. 100): $$\text{SP for 105 cm} = \frac{104.5}{95} \times 105 = \frac{104.5 \times 105}{95} = \frac{10972.5}{95} = \text{Rs. } 115.5$$

Step 4 — Calculate Profit %: $$\text{Profit %} = \frac{115.5 - 100}{100} \times 100 = \frac{15.5}{100} \times 100 = 15.5%$$

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3. Solution

Answer = Option C ✅

The merchant earns a profit of 15.5% by combining the free stock bonus on purchase, the false measure cheat on sales, and a 5% discount on the marked price.