A shopkeeper has 1000 kg of pepper. A part of this, he sells at 12% profit and 25% profit. Overall, he gains 18%. How many Kgs did he sell at 20% profit?

1. Break Down the Problem

We need to find out how many kilograms of pepper the shopkeeper sold at a 25% profit. To do this, we will set up equations based on the information given about the profits and the total quantity of pepper.

2. Relevant Concepts

Let:

• $x$ be the quantity sold at 12% profit.
• $y$ be the quantity sold at 25% profit.

We know the following:

1. Total quantity of pepper: $x + y = 1000$ kg.
2. Overall profit: $\frac{12x + 25y}{1000} = 18$.

3. Analysis and Detail

From the overall profit statement: $\text{Total selling price} = \text{Cost Price} + \text{Profit}$ $\text{Total selling price} = 1000 + 18\% \text{ of } 1000 = 1000 + 180 = 1180$

The selling price for each portion sold can be expressed in terms of $x$ and $y$: $\text{Selling Price from } x = x \cdot (1 + \frac{12}{100}) = 1.12x$ $\text{Selling Price from } y = y \cdot (1 + \frac{25}{100}) = 1.25y$

The total selling prices then gives us the equation: $1.12x + 1.25y = 1180$

4. Verify and Summarize

From the equations:

1. $x + y = 1000$
2. $1.12x + 1.25y = 1180$

We can solve these equations simultaneously.

Substituting $y = 1000 - x$ in the second equation: $1.12x + 1.25(1000 - x) = 1180$ $1.12x + 1250 - 1.25x = 1180$ $-0.13x + 1250 = 1180$ $-0.13x = -70$ $x = \frac{70}{0.13} \approx 538.46 \text{ kg}$

From $x + y = 1000$: $y = 1000 - 538.46 \approx 461.54 \text{ kg}$

Final Answer

The shopkeeper sold approximately 461.54 kg of pepper at a 25% profit.