Farah got married 8 years ago. Today her age is `1 2/7` times her age at the time of her marriage. At present her daughter's age is one-sixth of her age. What was her daughter's age 3 years ago?

Options

A. 6 years
B. 4 years
C. 3 years
D. None of these

Answer

To solve the problem step by step, let's denote Farah's present age as \( f \) and her daughter's present age as \( d \).

### Step 1: Establish the relationship between Farah's current age and her age at marriage.
Farah got married 8 years ago, so her age at that time was \( f - 8 \). According to the problem, her current age is \( 1 \frac{2}{7} \) times her age at the time of her marriage. We can express this as:

\[ f = \frac{9}{7} \times (f - 8) \]

### Step 2: Solve the equation for \( f \).
Now, let's solve the equation:

1. Start by multiplying both sides by 7 to eliminate the fraction:

\[ 7f = 9(f - 8) \]

2. Distribute the 9 on the right side:

\[ 7f = 9f - 72 \]

3. Rearranging gives:

\[ 7f - 9f = -72 \]

\[ -2f = -72 \]

4. Dividing both sides by -2:

\[ f = 36 \]

### Step 3: Find the daughter's present age.
According to the problem, the present age of Farah's daughter \( d \) is one-sixth of Farah's present age:

\[ d = \frac{1}{6} f \]

Substituting the value of \( f \):

\[ d = \frac{1}{6} \times 36 = 6 \]

### Step 4: Calculate the daughter's age 3 years ago.
To find the daughter's age 3 years ago, we subtract 3 from her current age:

\[ \text{Daughter's age 3 years ago} = d - 3 = 6 - 3 = 3 \]

### Final Answer:
Farah's daughter's age 3 years ago was **3 years**.

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