CAT 2021

Slot 1

QA

Question & Solution

1. Concept Used

• Topic: Ratio and Proportion / Linear Equations in Multiple Variables
• Formula: $$\text{If } X = Y = Z, \text{ then } X - Y = 0 \text{ and } Y - Z = 0$$

2. Calculation

Let the cost of one apple, one orange, and one mango be (a), (o), and (m) respectively.

We are given that all three baskets cost the same, so we can set up equations by equating them pairwise.

Equation 1: Equating Basket 1 and Basket 2: $$2a + 4o + 6m = a + 4o + 8m$$ $$2a - a + 4o - 4o + 6m - 8m = 0$$ $$a - 2m = 0$$ $$\boxed{a = 2m}$$

So, one apple is worth 2 mangoes.

Equation 2: Equating Basket 2 and Basket 3: $$a + 4o + 8m = 8o + 7m$$ $$a + 8m - 7m = 8o - 4o$$ $$a + m = 4o$$

Substituting (a = 2m): $$2m + m = 4o$$ $$3m = 4o$$ $$\boxed{o = \frac{3m}{4}}$$

So, one orange is worth (\frac{3}{4}) of a mango.

Finding the total cost in terms of mangoes:

Using Basket 1: (2a + 4o + 6m) $$= 2(2m) + 4\left(\frac{3m}{4}\right) + 6m$$ $$= 4m + 3m + 6m$$ $$= 13m$$

So the total cost of each basket equals the cost of 13 mangoes.

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3. Solution

Answer = Option B (13) ✅

The final calculated value is 13. A basket of only mangoes with the same cost as the other baskets would contain 13 mangoes.