A mathematics textbook costs Rs 2 more than a literature textbook. If the total cost of 5 literature textbooks is Rs 38 more than the total cost of 3 mathematics textbooks, what is the cost of one literature textbook?

Introduction / Context:
This question is a typical linear equation word problem involving prices of two different types of textbooks. It tests basic algebra skills in setting up equations from real-life style statements. We are given a relationship between the cost of a mathematics textbook and a literature textbook, and also a comparison between the total costs of multiple copies of each. The goal is to find the price of one literature textbook using these relationships.

Given Data / Assumptions:

• Let the cost of one literature textbook be L rupees.
• The cost of one mathematics textbook is 2 rupees more, so it is L + 2.
• The total cost of 5 literature textbooks is 38 rupees more than the total cost of 3 mathematics textbooks.
• We must find the value of L.

Concept / Approach:
We express both total costs in terms of L, then use the given difference of 38 rupees between these totals to form a linear equation. Specifically, the cost of 5 literature textbooks is 5L, and the cost of 3 mathematics textbooks is 3(L + 2). Given that 5L is 38 more than the latter, we write 5L = 3(L + 2) + 38. Solving this equation gives the price of one literature textbook. This approach is standard for word problems involving comparative costs.

Step-by-Step Solution:
Step 1: Let the cost of one literature textbook be L rupees. Step 2: Then the cost of one mathematics textbook is L + 2 rupees. Step 3: The total cost of 5 literature textbooks is 5L. Step 4: The total cost of 3 mathematics textbooks is 3(L + 2). Step 5: According to the problem, 5 literature textbooks cost Rs 38 more than 3 mathematics textbooks. Step 6: Form the equation: 5L = 3(L + 2) + 38. Step 7: Expand the right side: 3(L + 2) = 3L + 6, so the equation becomes 5L = 3L + 6 + 38. Step 8: Simplify: 5L = 3L + 44. Step 9: Subtract 3L from both sides: 2L = 44. Step 10: Divide both sides by 2: L = 22. Step 11: Therefore, one literature textbook costs Rs 22.

Verification / Alternative check:
Check using L = 22. Then one mathematics textbook costs 22 + 2 = 24 rupees. The cost of 5 literature textbooks is 5 * 22 = 110 rupees. The cost of 3 mathematics textbooks is 3 * 24 = 72 rupees. The difference is 110 − 72 = 38 rupees, which matches the given condition. This confirms that the cost of one literature textbook is correctly found as 22 rupees.

Why Other Options Are Wrong:
Option (a) 44: If literature cost were 44, numbers would not satisfy the given 38 rupee difference.
Option (c) 24: This would make mathematics textbooks cost 26, and totals would not differ by 38.
Option (d) 11: This would produce totals that differ by much less than 38 rupees.

Common Pitfalls:
Common mistakes include reversing the relationship (for example, assuming mathematics is cheaper than literature), misinterpreting the phrase "cost 38 rupees more," or forgetting to add 2 correctly when computing mathematics textbooks costs. Being careful with the language and assigning variables clearly helps prevent these issues.

Final Answer:
The cost of one literature textbook is Rs 22.