In a family, the average age of a father and a mother is 37 years. The average age of the father, mother, and their only daughter is 29 years. Find the age of the daughter.

Options

A. A)18 years
B. B)13 years
C. C)16 years
D. D)9 years

Answer

To find the age of the daughter, we can follow these steps:

### Step 1: Calculate the total age of the father and mother
Given that the average age of the father and mother is 37 years, we can use the formula for average:

\[ \text{Average} = \frac{\text{Total Age}}{\text{Number of People}} \]

Here, the number of people is 2 (father and mother). Therefore, we can write:

\[ 37 = \frac{\text{Total Age of Father and Mother}}{2} \]

Multiplying both sides by 2 gives:

\[ \text{Total Age of Father and Mother} = 37 \times 2 = 74 \text{ years} \]

### Step 2: Calculate the total age of the father, mother, and daughter
Next, we know that the average age of the father, mother, and daughter is 29 years. Again, using the average formula:

\[ 29 = \frac{\text{Total Age of Father, Mother, and Daughter}}{3} \]

Multiplying both sides by 3 gives:

\[ \text{Total Age of Father, Mother, and Daughter} = 29 \times 3 = 87 \text{ years} \]

### Step 3: Find the age of the daughter
Now, we have the total age of the father and mother (74 years) and the total age of the father, mother, and daughter (87 years). To find the age of the daughter, we subtract the total age of the father and mother from the total age of the father, mother, and daughter:

\[ \text{Age of Daughter} = \text{Total Age of Father, Mother, and Daughter} - \text{Total Age of Father and Mother} \]

Substituting the values:

\[ \text{Age of Daughter} = 87 - 74 = 13 \text{ years} \]

### Conclusion
Thus, the age of the daughter is **13 years**.

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