Five bottles cost as much as two bags. The combined cost of 15 bottles and 4 bags is Rs 2000. Based on this information, what is the price of a single bag in rupees?

Introduction / Context:
This is a standard linear equations problem involving prices of two items. You know the relationship between the cost of bottles and bags, and the total cost of a combination of these items. Using algebra, you can set up equations in terms of the price of one bottle and one bag, and then find the unknown price. Such questions appear frequently in aptitude tests to assess comfort with forming and solving simple equations from word statements.

Given Data / Assumptions:

• Five bottles cost as much as two bags.
• Total cost of 15 bottles and 4 bags is Rs 2000.
• Prices of bottles and bags are constant and positive.
• We must find the price of one bag.

Concept / Approach:
Let the price of one bottle be B rupees and the price of one bag be A rupees. The first statement gives us one linear relationship between A and B. The second statement gives us a second equation involving the total cost of a specific combination of bottles and bags. From the first relation, we can express B in terms of A, and then substitute into the second equation to solve for A directly. This avoids dealing with two unknowns at the end of the problem.

Step-by-Step Solution:
Let A = price of one bag in rupees. Let B = price of one bottle in rupees. Given that five bottles cost as much as two bags: 5B = 2A. From this, express B in terms of A: B = (2/5)A. We are also told that 15 bottles and 4 bags together cost Rs 2000. So 15B + 4A = 2000. Substitute B = (2/5)A into this equation. 15 * (2/5)A + 4A = 2000. Compute 15 * (2/5)A = (30/5)A = 6A. So the equation becomes 6A + 4A = 2000. Combine like terms: 10A = 2000. Solve for A: A = 2000 / 10 = 200. Therefore, the price of one bag is Rs 200.

Verification / Alternative check:
We can check our result by computing the price of one bottle and verifying the total cost. With A = 200, B = (2/5) * 200 = 80. Now compute the cost of 15 bottles and 4 bags: 15 * 80 + 4 * 200 = 1200 + 800 = 2000. This matches the given total cost, so the value A = 200 is correct.

Why Other Options Are Wrong:
If you assume A = 215, 240, 250, or 300 and then compute the implied bottle price B from 5B = 2A, substituting into 15B + 4A will not give exactly 2000. These alternative values arise only from algebraic errors or misinterpretation of the initial relation between bottles and bags.

Common Pitfalls:
Common mistakes include reversing the relationship and writing 5B = A instead of 5B = 2A, or forgetting to multiply the bottle price by 15 when forming the total cost equation. Another pitfall is dropping a factor when simplifying 15 * (2/5)A. Writing equations carefully from the word statement and double checking each step helps avoid these issues.

Final Answer:
The price of a single bag is Rs 200.