In a club, the average age of the members is 30 years, the average age of the male members is 34 years and that of the female members is 26 years. The percentage of the male members is

Options

A. 50%
B. 60%
C. 30%
D. 40%

Answer

To find the percentage of male members in the club, we can use the concept of allegations. Here’s the step-by-step solution:

### Step 1: Understand the given data
- Average age of all members (A) = 30 years
- Average age of male members (M) = 34 years
- Average age of female members (F) = 26 years

### Step 2: Set up the allegation
We will use the allegation method to find the ratio of male to female members. The formula for the allegation is:

\[ \text{Ratio of Male to Female} = \frac{F - A}{A - M} \]

### Step 3: Calculate the differences
- Difference between the average age of females and the overall average:
\[ F - A = 26 - 30 = -4 \]
- Difference between the overall average and the average age of males:
\[ A - M = 30 - 34 = -4 \]

### Step 4: Set up the ratio
Now we can substitute these values into the ratio:
\[ \text{Ratio of Male to Female} = \frac{30 - 26}{34 - 30} = \frac{4}{4} = 1:1 \]

### Step 5: Calculate the total parts
This ratio indicates that for every 1 male member, there is 1 female member. Therefore, the total parts are:
- Male members = 1 part
- Female members = 1 part
- Total members = 1 + 1 = 2 parts

### Step 6: Calculate the percentage of male members
To find the percentage of male members, we use the formula:
\[ \text{Percentage of Male Members} = \left(\frac{\text{Number of Male Members}}{\text{Total Members}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage of Male Members} = \left(\frac{1}{2}\right) \times 100 = 50\% \]

### Final Answer
The percentage of male members in the club is **50%**.

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