Swati ate 1/2 of the candies she had and gave rest to Jeny. Jeny kept 8 of the candies and gave rest of the 10 candies to Sakshi. How many candies did Swati eat?

Options

A. 18
B. 24
C. 72
D. 36

Answer

To solve the problem step by step, let's break it down:

1. **Define the total number of candies Swati had**:
Let the total number of candies Swati had be represented by \( X \).

2. **Determine how many candies Swati ate**:
Swati ate half of the candies she had, which can be expressed as:
\[ \text{Candies eaten by Swati} = \frac{X}{2} \]

3. **Determine how many candies Swati gave to Jeny**:
Since Swati ate half, she gave the other half to Jeny:
\[ \text{Candies given to Jeny} = \frac{X}{2} \]

4. **Understand what Jeny did with the candies**:
Jeny kept 8 candies and gave the remaining to Sakshi. According to the problem, Jeny gave 10 candies to Sakshi. Therefore, the total number of candies Jeny had can be calculated as:
\[ \text{Total candies Jeny had} = \text{Candies kept by Jeny} + \text{Candies given to Sakshi} = 8 + 10 = 18 \]

5. **Set up the equation**:
Since we know that Jeny received half of Swati's candies, we can set up the equation:
\[ \frac{X}{2} = 18 \]

6. **Solve for \( X \)**:
To find \( X \), multiply both sides of the equation by 2:
\[ X = 18 \times 2 = 36 \]

7. **Calculate how many candies Swati ate**:
Now that we know the total number of candies Swati had, we can find out how many she ate:
\[ \text{Candies eaten by Swati} = \frac{X}{2} = \frac{36}{2} = 18 \]

Thus, Swati ate **18 candies**.