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 ?

Correct Answer: 10

Let us solve this step-by-step to find the number of eucalyptus trees in the garden.

Step 1: Find the total number of trees in the garden.
We are given that one-sixth of the total trees in the garden are neem trees, and there are 5 neem trees in total.

Let $T$ be the total number of trees in the garden.

According to the question:

$\frac{1}{6}\times T=5$

Multiplying both sides by 6:

$T=5\times 6=30$

So, the total number of trees in the garden is 30.

Step 2: Find the number of Ashoka trees.
We are given that half of the trees are Ashoka trees.

$\text{Number of Ashoka trees}=\frac{1}{2}\times 30=15$

Step 3: Find the number of eucalyptus trees.
The remaining trees are eucalyptus trees. To find their number, subtract the number of neem trees and Ashoka trees from the total number of trees:

$\text{Number of eucalyptus trees}=\text{Total trees}-(\text{Neem trees}+\text{Ashoka trees})$

$\text{Number of eucalyptus trees}=30-(5+15)$

$\text{Number of eucalyptus trees}=30-20=10$

Thus, there are 10 eucalyptus trees in the garden.