📚 Part of: Algebra And Indian History Mcq Quiz

The cost price of a shirt and a pair of trousers is Rs 371. If the shirt costs 12% more than the trousers, find the cost price of the trousers

Category: Miscellaneous Indian Gk

Correct Answer: B) 175.

Exam Relevance: CAT, MAT, GRE, GMAT, Bank PO, SSC CGL

Difficulty: Moderate

Concept notes:

In this problem, we need to find the cost price of the trousers given the total cost price of a shirt and trousers and the percentage increase of the shirt's cost over the trousers. We use algebraic equations to represent the relationship between the cost prices and solve for the unknown.

Common Mistakes:
  • Misinterpreting the percentage increase as a direct addition to the cost of the trousers.
  • Incorrectly setting up the algebraic equation to represent the relationship between the cost of the shirt and trousers.
  • Forgetting to solve for the cost of the trousers after setting up the equation.
Explanation:

To solve this problem, we need to set up an algebraic equation based on the given information. Let's denote the cost price of the trousers as \( T \) and the cost price of the shirt as \( S \).

According to the problem, the total cost price of the shirt and trousers is Rs 371. Therefore, we can write the equation:

\[ S + T = 371 \]

We are also given that the shirt costs 12% more than the trousers. This means:

\[ S = T + 0.12T \]

\[ S = 1.12T \]

Now, we substitute \( S = 1.12T \) into the first equation:

\[ 1.12T + T = 371 \]

\[ 2.12T = 371 \]

To find the cost price of the trousers, we solve for \( T \):

\[ T = \frac{371}{2.12} \]

\[ T = 175 \]

Thus, the cost price of the trousers is Rs 175.

To verify, we calculate the cost of the shirt:

\[ S = 1.12 \times 175 = 196 \]

Adding the cost of the shirt and trousers:

\[ 175 + 196 = 371 \]

This confirms that the cost price of the trousers is indeed Rs 175, and the correct answer is (B) 175.

This problem demonstrates the application of algebraic equations and percentage calculations to solve real-world problems involving cost prices. It is important to set up the equations correctly and solve them step-by-step to ensure accuracy.

Option Analysis:
  • Option A: This option is incorrect. If the cost of the trousers were Rs 150, the cost of the shirt would be 12% more, which is Rs 168. The total cost would then be Rs 318, not Rs 371. This does not satisfy the given conditions of the problem.
  • Option B: This option is correct. If the cost of the trousers is Rs 175, the cost of the shirt would be 12% more, which is Rs 196. The total cost would then be Rs 371, which matches the given total cost. This satisfies the conditions of the problem.
  • Option C: This option is incorrect. If the cost of the trousers were Rs 160, the cost of the shirt would be 12% more, which is Rs 179.20. The total cost would then be Rs 339.20, not Rs 371. This does not satisfy the given conditions of the problem.
  • Option D: This option is incorrect. If the cost of the trousers were Rs 200, the cost of the shirt would be 12% more, which is Rs 224. The total cost would then be Rs 424, not Rs 371. This does not satisfy the given conditions of the problem.
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