One-sixth of the trees in a garden are neem trees. Half of the trees are Ashoka trees and the remaining are eucalyptus trees. If the number of neem trees is five, how many eucalyptus trees are there in the garden ?

Question

Accepted Answer

To determine the number of eucalyptus trees in the garden, we need to analyze the information given in the question:

1. **Neem Trees**: One-sixth of the trees in the garden are neem trees. It is given that the number of neem trees is five. Therefore, if one-sixth of the total number of trees is five, we can calculate the total number of trees as follows:

$$
   \frac{1}{6} \times \text{Total Trees} = 5
   $$

Solving for the total number of trees:

$$
   \text{Total Trees} = 5 \times 6 = 30
   $$

2. **Ashoka Trees**: Half of the trees are Ashoka trees. Therefore, the number of Ashoka trees is:

$$
   \frac{1}{2} \times 30 = 15
   $$

3. **Eucalyptus Trees**: The remaining trees are eucalyptus trees. To find the number of eucalyptus trees, we subtract the number of neem and Ashoka trees from the total number of trees:

$$
   \text{Eucalyptus Trees} = \text{Total Trees} - (\text{Neem Trees} + \text{Ashoka Trees})
   $$

$$
   \text{Eucalyptus Trees} = 30 - (5 + 15) = 30 - 20 = 10
   $$

Thus, the number of eucalyptus trees in the garden is 10, which corresponds to Option 2.

**Explanation of Incorrect Options:**

- **Option 1 (5)**: This option is incorrect because if there were only 5 eucalyptus trees, the total number of trees would not add up to 30 when considering the given numbers of neem and Ashoka trees.

- **Option 3 (15)**: This option is incorrect because having 15 eucalyptus trees would exceed the total number of trees when combined with the neem and Ashoka trees.

- **Option 4 (20)**: This option is incorrect because having 20 eucalyptus trees would also exceed the total number of trees when combined with the neem and Ashoka trees.

Therefore, the correct answer is Option 2, which is 10 eucalyptus trees.