CAT 2017

Slot 1

QA

Question & Solution

1. Concept Used

• Topic: Profit and Loss — Relationship between Cost Price, Retail (Marked) Price, Discount, and Profit
• Formula: $$\text{Selling Price} = \text{Marked Price} \times \left(1 - \frac{\text{Discount%}}{100}\right) = \text{Cost Price} \times \left(1 + \frac{\text{Profit%}}{100}\right)$$

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2. Calculation

Let the Retail (Marked) Price be $$M$$ and the Cost Price be $$C$$.

We are told that a discount of 15% on the retail price still yields a profit of 2%. This means the selling price equals both:

$$0.85M = 1.02C$$

Solving for $$M$$ in terms of $$C$$:

$$M = \frac{1.02C}{0.85} = \frac{102C}{85} = \frac{6C}{5} = 1.20C$$

So the Retail Price $$M = 1.20C$$, which is exactly 20% above the cost price.

Now, for the seller to make a profit of 20%, she needs to sell at:

$$\text{Required Selling Price} = 1.20C$$

Since we already established that $$M = 1.20C$$, selling at the retail price (no discount) directly gives a profit of exactly 20%.

Let's verify the other options are incorrect:

• 5% discount: $$0.95M = 0.95 \times 1.20C = 1.14C$$ → only 14% profit ❌
• 2% discount: $$0.98M = 0.98 \times 1.20C = 1.176C$$ → only 17.6% profit ❌
• Increase retail price by 2%: $$1.02M = 1.02 \times 1.20C = 1.224C$$ → 22.4% profit ❌
• Sell at retail price: $$M = 1.20C$$ → exactly 20% profit ✅

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3. Solution

Answer = Option 4 ✅

The retail price is already 1.20 times the cost price, so selling at the retail price (i.e., giving no discount) ensures exactly a 20% profit.