CAT 2017

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Percentage — Successive Reduction
• Formula: $$\text{Shirts for Export} = x \times \left(1 - \frac{15}{100}\right) \times \left(1 - \frac{20}{100}\right)$$

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2. Calculation

Let the total number of shirts produced in the factory be $$x$$.

Step 1 — Remove Defective Shirts:

$$15%$$ of shirts are defective, so the number of non-defective (good) shirts is:

$$\text{Non-defective shirts} = x - 0.15x = 0.85x$$

Step 2 — Remove Shirts Sold in Domestic Market:

$$20%$$ of the non-defective shirts are sold in the domestic market. So the shirts remaining for export are the other $$80%$$ of non-defective shirts:

$$\text{Shirts for Export} = 0.80 \times 0.85x = 0.68x$$

Step 3 — Set Equal to Given Value and Solve:

We are told the shirts left for export = 8840:

$$0.68x = 8840$$

$$x = \frac{8840}{0.68} = \frac{8840 \times 100}{68} = \frac{884000}{68} = 13000$$

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3. Solution

Answer = Option B ✅

The total number of shirts produced in the factory is 13,000.