Let's define the variables:
Let the cost price of the first product be Rs. x, and its selling price be Rs. S₁.
Let the cost price of the second product be Rs. y, and its selling price be Rs. S₂.

Given Conditions:

1. Difference between selling prices:
   $S₁ - S₂ = 200$
2. Difference between cost prices:
   $x - y = 100$
3. First product is sold at 10% profit:
   $S₁ = x + 10\% \text{ of } x = x + 0.1x = 1.1x$
4. Second product is sold at 20% loss:
   $S₂ = y - 20\% \text{ of } y = y - 0.2y = 0.8y$

Step 1: Express the given equation using these formulas

$1.1x - 0.8y = 200$ $x - y = 100$

Step 2: Solve the System of Equations

We have:

1. 1.1x - 0.8y = 200
2. x - y = 100

From equation (2):
$x = y + 100$

Substituting in equation (1):

$1.1(y + 100) - 0.8y = 200$

Expanding:

$1.1y + 110 - 0.8y = 200$

$0.3y + 110 = 200$

$0.3y = 90$

$y = 300$

Now, substituting $y = 300$ in $x = y + 100$:

$x = 300 + 100 = 400$

Final Answer:

• Cost price of first product = Rs. 400
• Cost price of second product = Rs. 300

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Would you like a more detailed explanation or alternative method?

Here are 5 related questions to explore further:

1. If both products were sold at a 10% profit, what would be the new selling prices?
2. What would be the new cost prices if the selling price difference was Rs. 300 instead of Rs. 200?
3. How would the result change if the first product was sold at a 15% profit instead of 10%?
4. If both products were sold at no profit or loss, what would be their selling prices?
5. What is the overall profit or loss if 5 units of each product were sold under the given conditions?

Math Tip:

When dealing with profit and loss problems, always express profit or loss as a percentage of the cost price, not the selling price.