In a group of 108 persons, the ratio of number of males and females is 5:4. The average height of the males is 158.7 cm and that of the females is x cm. If the average height of all the persons in the group is 155.5 cm , then the values of x is :

Options

A. 151.5
B. 150.8
C. 152.2
D. 153.4

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the number of males and females
Given the ratio of males to females is 5:4, we can find the number of males and females in the group of 108 persons.

Let the number of males be \(5k\) and the number of females be \(4k\).

The total number of persons is:
\[ 5k + 4k = 108 \]
\[ 9k = 108 \]
\[ k = \frac{108}{9} = 12 \]

Thus, the number of males is:
\[ 5k = 5 \times 12 = 60 \]
And the number of females is:
\[ 4k = 4 \times 12 = 48 \]

### Step 2: Calculate the total height of males
The average height of males is given as 158.7 cm. Therefore, the total height of all males can be calculated as:
\[ \text{Total height of males} = \text{Number of males} \times \text{Average height of males} \]
\[ = 60 \times 158.7 = 9522 \text{ cm} \]

### Step 3: Set up the equation for the average height of the group
The average height of all persons in the group is given as 155.5 cm. Therefore, the total height of all persons is:
\[ \text{Total height of all persons} = \text{Total number of persons} \times \text{Average height} \]
\[ = 108 \times 155.5 = 16794 \text{ cm} \]

### Step 4: Calculate the total height of females
Let the average height of females be \(x\) cm. The total height of females can be expressed as:
\[ \text{Total height of females} = \text{Number of females} \times \text{Average height of females} \]
\[ = 48 \times x \]

### Step 5: Set up the equation for total height
Now, we can set up the equation for total height:
\[ \text{Total height of males} + \text{Total height of females} = \text{Total height of all persons} \]
\[ 9522 + 48x = 16794 \]

### Step 6: Solve for \(x\)
Now, we will isolate \(x\):
\[ 48x = 16794 - 9522 \]
\[ 48x = 7262 \]
\[ x = \frac{7262}{48} = 151.5 \text{ cm} \]

### Final Answer
Thus, the average height of females \(x\) is:
\[ \boxed{151.5 \text{ cm}} \]