At present Geeta is eight times her daughter's age. Eight years from now, the ratio of the ages of Geeta and her daughter will be ` 10 : 3` respectively. What is Geeta's present age ?

Options

A. 32 years
B. 40 years
C. 36 years
D. Can't say

Explanation

To solve the problem step by step, let's denote the daughter's current age as \( x \). According to the problem:

1. **Geeta's Current Age**: Since Geeta is currently eight times her daughter's age, we can express Geeta's age as:
\[ \text{Geeta's age} = 8x \]

2. **Ages Eight Years from Now**: In eight years, the daughter's age will be:
\[ \text{Daughter's age in 8 years} = x + 8 \]
And Geeta's age will be:
\[ \text{Geeta's age in 8 years} = 8x + 8 \]

3. **Setting Up the Ratio**: According to the problem, the ratio of Geeta's age to her daughter's age in eight years will be \( 10:3 \). Therefore, we can set up the equation:
\[ \frac{8x + 8}{x + 8} = \frac{10}{3} \]

4. **Cross-Multiplying**: To eliminate the fraction, we cross-multiply:
\[ 3(8x + 8) = 10(x + 8) \]

5. **Expanding Both Sides**: Now, we expand both sides of the equation:
\[ 24x + 24 = 10x + 80 \]

6. **Rearranging the Equation**: Next, we rearrange the equation to isolate \( x \):
\[ 24x - 10x = 80 - 24 \]
\[ 14x = 56 \]

7. **Solving for \( x \)**: Now, we divide both sides by 14 to find \( x \):
\[ x = \frac{56}{14} = 4 \]

8. **Finding Geeta's Present Age**: Finally, we substitute \( x \) back into the equation for Geeta's age:
\[ \text{Geeta's age} = 8x = 8 \times 4 = 32 \]

Thus, Geeta's present age is **32 years**.