27. A shirt costs ₹12 more than a belt. The total cost of 2 such shirts and 5 such belts is ₹161. What is the cost of a belt?

A. ₹32
B. ₹34

(Note: Add A and B options instead of C and D for clarity)



Answer :

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.