To solve the problem, let's denote the cost of a belt by \( b \). According to the problem, the cost of a shirt is \( ₹12 \) more than the cost of the belt. Therefore, the cost of a shirt can be expressed as \( b + 12 \).
The total cost of 2 such shirts and 5 such belts is given to be ₹161. We can write this as an equation:
[tex]\[ 2 \times (b + 12) + 5b = 161 \][/tex]
Now let's simplify and solve this equation step by step:
1. Distribute the 2 in the expression \( 2 \times (b + 12) \):
[tex]\[ 2b + 24 + 5b = 161 \][/tex]
2. Combine like terms on the left side of the equation:
[tex]\[ 7b + 24 = 161 \][/tex]
3. Subtract 24 from both sides to isolate terms involving \( b \):
[tex]\[ 7b = 161 - 24 \][/tex]
[tex]\[ 7b = 137 \][/tex]
4. Divide both sides by 7 to solve for \( b \):
[tex]\[ b = \frac{137}{7} \][/tex]
5. Perform the division:
[tex]\[ b = 19.571428571428573 \][/tex]
Thus, the cost of a belt is approximately ₹19.57.
None of the provided options, (C) ₹32 or (D) ₹34, matches the calculated price, so neither provided option accurately represents the correct cost of the belt.
