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The problem in the image asks the following:

**Problem Statement:**
How many kilograms of salt costing Rs. 42 per kilogram must a man mix with 25 kg of salt costing Rs. 24 per kilogram, such that on selling the mixture at Rs. 40 per kilogram, there is a gain of 25% on the outlay?

### Solution:

Let the amount of salt costing Rs. 42 per kg be **x kg**.

The total amount of salt after mixing = \( x + 25 \) kg.

#### Cost price:
1. The cost of **x** kg of salt at Rs. 42 per kg = \( 42x \) Rs.
2. The cost of 25 kg of salt at Rs. 24 per kg = \( 25 \times 24 = 600 \) Rs.

So, the total cost price = \( 42x + 600 \) Rs.

#### Selling price:
The mixture is sold at Rs. 40 per kg. So, the total selling price = \( (x + 25) \times 40 = 40(x + 25) = 40x + 1000 \) Rs.

#### Profit condition:
There is a gain of 25%. The gain is on the outlay (total cost price). So, the selling price should be 25% more than the cost price.

\[
\text{Selling price} = \text{Cost price} + 25\% \text{ of cost price}
\]
\[
40x + 1000 = (42x + 600) + 0.25 \times (42x + 600)
\]

Simplifying:
\[
40x + 1000 = (42x + 600) + 0.25 \times (42x + 600)
\]
First, calculate the 25% of the cost price:
\[
0.25 \times (42x + 600) = 0.25 \times 42x + 0.25 \times 600 = 10.5x + 150
\]
Now, substitute this into the equation:
\[
40x + 1000 = (42x + 600) + (10.5x + 150)
\]
\[
40x + 1000 = 52.5x + 750
\]
Rearranging:
\[
1000 - 750 = 52.5x - 40x
\]
\[
250 = 12.5x
\]
\[
x = \frac{250}{12.5} = 20
\]

### Conclusion:
The man must mix **20 kg** of salt costing Rs. 42 per kg with the 25 kg of salt costing Rs. 24 per kg.

---

Would you like more details on any step or have any questions?

### Further Exploration:
1. What would the mixture cost per kg if there were no profit?
2. How much would the total outlay be if the man used 30 kg of the Rs. 42 per kg salt?
3. What if the selling price was Rs. 45 per kg? How much salt should be mixed then?
4. What is the percentage gain if the selling price is Rs. 50 per kg?
5. How would the solution change if the gain percentage were reduced to 15%?

**Tip:** When solving such problems, the relationship between cost price, selling price, and profit can be simplified by using percentage-based equations.

How many kilograms of salt costing Rs. 42 per kilogram must a man mix with 25 kg of salt costing Rs. 24 per kilogram, such that on selling the mixture at Rs. 40 per kilogram, there is a gain of 25% on the outlay?

Learn how to determine how many kilograms of salt costing Rs. 42 per kilogram must be mixed with 25 kg of salt costing Rs. 24 per kilogram to achieve a 25% gain when selling the mixture at Rs. 40 per kilogram. This problem involves profit and loss calculations, mixture equations, and is ideal for students in Grades 9-11.

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