Directions : Study the following information carefully and answer the questions given below:
There are 450 coupons which can be used in Pedicure and Hair cutting. The ratio of Males to Females who use their coupons in Hair cutting is 13: 7. The number of males who use their coupons in Pedicure is 72 more than the number of females who use their coupon in Hair cutting. Total number of males who use their coupon in Pedicure and Hair cutting together is 174 more than the total number of females who use their coupon in Pedicure and Hair cutting together.
Out of the males who use their coupons in Hair cutting`25%` belong to city A. Then find the number of males who use their coupons in Hair cutting and doesn't belong to city A.

Options

A. None of these given as option
B. 108
C. 126
D. 117

Answer

To solve the problem step by step, we will break down the information provided and use algebraic equations to find the required values.

### Step 1: Define Variables
Let:
- The number of males using coupons for hair cutting = \( 13x \)
- The number of females using coupons for hair cutting = \( 7x \)
- The number of females using coupons for pedicure = \( y \)
- The number of males using coupons for pedicure = \( 7x + 72 \) (since it is given that this is 72 more than the number of females using hair cutting)

### Step 2: Total Coupons Equation
The total number of coupons used is 450. Therefore, we can write the equation:
\[ (13x + 7x + y + (7x + 72)) = 450 \]
This simplifies to:
\[ 27x + y + 72 = 450 \]
Subtracting 72 from both sides gives:
\[ 27x + y = 378 \quad \text{(Equation 1)} \]

### Step 3: Difference in Total Users
It is given that the total number of males using their coupons is 174 more than the total number of females using their coupons. This gives us the equation:
\[ (13x + (7x + 72)) = (y + 7x) + 174 \]
This simplifies to:
\[ 20x + 72 = y + 7x + 174 \]
Rearranging gives:
\[ 20x + 72 - 7x - 174 = y \]
This simplifies to:
\[ 13x - y = 102 \quad \text{(Equation 2)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( 27x + y = 378 \)
2. \( 13x - y = 102 \)

We can add these two equations to eliminate \( y \):
\[ (27x + y) + (13x - y) = 378 + 102 \]
This simplifies to:
\[ 40x = 480 \]
Thus, solving for \( x \):
\[ x = \frac{480}{40} = 12 \]

### Step 5: Calculate Number of Males and Females
Now we can find the number of males and females:
- Number of males using hair cutting = \( 13x = 13 \times 12 = 156 \)
- Number of females using hair cutting = \( 7x = 7 \times 12 = 84 \)
- Number of males using pedicure = \( 7x + 72 = 84 + 72 = 156 \)
- Number of females using pedicure = \( y \)

Using Equation 1 to find \( y \):
\[ 27(12) + y = 378 \implies 324 + y = 378 \implies y = 54 \]
So, the number of females using pedicure = 54.

### Step 6: Find Males not from City A
Out of the males who use their coupons in hair cutting, 25% belong to City A. Therefore, the number of males from City A is:
\[ 0.25 \times 156 = 39 \]
Thus, the number of males who use their coupons in hair cutting and do not belong to City A is:
\[ 156 - 39 = 117 \]

### Final Answer
The number of males who use their coupons in hair cutting and do not belong to City A is **117**.