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.
Males who use their coupon in Pedicure are what percent of the Males who use their coupons in Hair cutting?

Options

A. `200%`
B. `100%`
C. none of these
D. `0`%`

Answer

To solve the problem step by step, we will define variables based on the information provided and set up equations accordingly.

### Step 1: Define Variables
Let:
- \( M_H \) = Number of males using coupons for Hair cutting
- \( F_H \) = Number of females using coupons for Hair cutting
- \( M_P \) = Number of males using coupons for Pedicure
- \( F_P \) = Number of females using coupons for Pedicure

### Step 2: Set Up Ratios
According to the problem, the ratio of males to females who use their coupons for Hair cutting is 13:7. This can be expressed as:
\[ \frac{M_H}{F_H} = \frac{13}{7} \]
Let \( M_H = 13x \) and \( F_H = 7x \) for some integer \( x \).

### Step 3: Express Males in Pedicure
The problem states that the number of males who use their coupons for Pedicure is 72 more than the number of females who use their coupons for Hair cutting. Thus, we can write:
\[ M_P = F_H + 72 = 7x + 72 \]

### Step 4: Total Males and Females
The total number of males using coupons for both services is:
\[ M_H + M_P = 13x + (7x + 72) = 20x + 72 \]
The total number of females using coupons for both services is:
\[ F_H + F_P = 7x + F_P \]
According to the problem, the total number of males is 174 more than the total number of females:
\[ 20x + 72 = (7x + F_P) + 174 \]
This simplifies to:
\[ 20x + 72 = 7x + F_P + 174 \]
Rearranging gives:
\[ 20x - 7x + 72 - 174 = F_P \]
\[ 13x - 102 = F_P \]

### Step 5: Total Coupons
We know the total number of coupons is 450:
\[ M_H + M_P + F_H + F_P = 450 \]
Substituting the expressions we have:
\[ (13x) + (7x + 72) + (7x) + (13x - 102) = 450 \]
This simplifies to:
\[ 40x - 30 = 450 \]
Adding 30 to both sides:
\[ 40x = 480 \]
Dividing by 40:
\[ x = 12 \]

### Step 6: Calculate Individual Values
Now we can find the number of males and females:
- \( M_H = 13x = 13 \times 12 = 156 \)
- \( F_H = 7x = 7 \times 12 = 84 \)
- \( M_P = 7x + 72 = 84 + 72 = 156 \)
- \( F_P = 13x - 102 = 156 - 102 = 54 \)

### Step 7: Calculate the Required Percentage
We need to find what percent the number of males using their coupons for Pedicure is of the number of males using their coupons for Hair cutting:
\[ \text{Percentage} = \left( \frac{M_P}{M_H} \right) \times 100 = \left( \frac{156}{156} \right) \times 100 = 100\% \]

Thus, the answer is **100%**.