Amrita and her grandmother both had birthdays on same day. The sum of their ages is 100 years. Amrita's grandmother's age is 4 times her age. Find their present ages.

Options

A. 25 years, 75 years
B. 20 years, 80 years
C. 22 years, 88 years
D. 25 years, 100 years

Answer

To solve the problem, we need to find the present ages of Amrita and her grandmother given that their combined age is 100 years and that Amrita's grandmother is 4 times Amrita's age.

### Step-by-Step Solution:

1. **Define Variables**:
- Let Amrita's age be \( A \).
- Then, her grandmother's age will be \( 4A \) (since her grandmother's age is 4 times Amrita's age).

2. **Set Up the Equation**:
- According to the problem, the sum of their ages is 100 years. Therefore, we can write the equation:
\[ A + 4A = 100 \]

3. **Combine Like Terms**:
- Combine the terms on the left side of the equation:
\[ 5A = 100 \]

4. **Solve for Amrita's Age**:
- To find \( A \), divide both sides of the equation by 5:
\[ A = \frac{100}{5} = 20 \]

5. **Find Grandmother's Age**:
- Now that we have Amrita's age, we can find her grandmother's age:
\[ \text{Grandmother's age} = 4A = 4 \times 20 = 80 \]

6. **Conclusion**:
- Amrita's present age is 20 years, and her grandmother's present age is 80 years.

### Final Answer:
- Amrita's age: 20 years
- Grandmother's age: 80 years