CAT 2024 Slot 1 QA Question 15

Multiple choice (+3 / −1) · Algebra · Linear Equation · Try it, then check the answer and solution below.

CAT 2024 Slot 1QAAlgebra • Linear EquationEasy

A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

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Official Convenor Answer Key: A

Verified Solution:

### Core Concept The problem involves sequential transactions where the shop sells half of the remaining grains plus an additional 3 kg each time. To find the initial quantity, we can work backwards from the final quantity, which is zero after the third customer.

### Step-by-Step Solution

After the Third Customer:

Let

X

be the quantity before the third sale.

Sold:

\frac{X}{2} + 3

Remaining:

X - \left( \frac{X}{2} + 3 \right) = 0

Simplify:

\frac{X}{2} - 3 = 0 \Rightarrow X = 6

kg.

After the Second Customer:

Let

Y

be the quantity before the second sale.

Sold:

\frac{Y}{2} + 3

Remaining: \( Y - \left( \frac{Y}{2

Answer and solution

Answer: A) 42

### Step-by-Step Solution

After the Third Customer:

Let

X

be the quantity before the third sale.

Sold:

\frac{X}{2} + 3

Remaining:

X - \left( \frac{X}{2} + 3 \right) = 0

Simplify:

\frac{X}{2} - 3 = 0 \Rightarrow X = 6

kg.

After the Second Customer:

Let

Y

be the quantity before the second sale.

Sold:

\frac{Y}{2} + 3

Remaining: \( Y - \left( \frac{Y}{2

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