Explanations:To solve the problem of finding the cost price of the trousers given that the total cost of a shirt and a pair of trousers is Rs 371 and the shirt costs 12% more than the trousers, we can set up a system of equations. Let's denote the cost price of the trousers as \( T \) and the cost price of the shirt as \( S \).
The relationship between the shirt and trousers prices is given by the statement that the shirt costs 12% more than the trousers. This can be expressed mathematically as:
\[ S = 1.12T \]
This equation tells us that the cost of the shirt is 1.12 times the cost of the trousers.
We are also given that the total cost of the shirt and trousers is Rs 371. This can be written as:
\[ S + T = 371 \]
Now, we can substitute the expression for \( S \) from the first equation into the second equation:
\[ 1.12T + T = 371 \]
Combining like terms, we get:
\[ 2.12T = 371 \]
To find the value of \( T \), we divide both sides of the equation by 2.12:
\[ T = \frac{371}{2.12} \]
Performing the division, we get:
\[ T = 175 \]
Thus, the cost price of the trousers is Rs 175.
To verify, we can calculate the cost of the shirt using the relationship \( S = 1.12T \):
\[ S = 1.12 \times 175 = 196 \]
Adding the cost of the shirt and the trousers, we get:
\[ 175 + 196 = 371 \]
This confirms that the total cost is indeed Rs 371, verifying our solution.
Therefore, the cost price of the trousers is Rs 175.