CAT 2017Slot 2QAQuestion & Solution

ArithmeticEasy

Question

The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30% Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is

Options

1500

2000

2500

3000

Solution

1. Concept Used

Topic: Profit and Loss — Successive Percentage Increases
Formula: $$\text{Final Price} = \text{Cost Price} \times \left(1 + \frac{p_1}{100}\right) \times \left(1 + \frac{p_2}{100}\right) \times \left(1 + \frac{p_3}{100}\right)$$

2. Calculation

Let the manufacturing cost of the table be $$x$$.

The manufacturer sells to the wholesaler at a 10% profit, so the wholesaler's cost becomes: $$x \times 1.1$$

The wholesaler sells to the retailer at a 30% profit, so the retailer's cost becomes: $$x \times 1.1 \times 1.3$$

The retailer sells to the customer at a 50% profit, so the customer pays: $$x \times 1.1 \times 1.3 \times 1.5$$

We are given that the customer pays Rs 4290, so: $$x \times 1.1 \times 1.3 \times 1.5 = 4290$$

Calculating the product of the multipliers: $$1.1 \times 1.3 = 1.43$$ $$1.43 \times 1.5 = 2.145$$

Now solving for $$x$$: $$x = \frac{4290}{2.145}$$ $$x = \frac{4290 \times 1000}{2145}$$ $$x = \frac{4290000}{2145} = 2000$$

3. Solution

Answer = Option 2 ✅

The final calculated manufacturing cost is Rs 2000.