A farmer wants to plant 95 mango trees, 171 banyan trees, and 152 banana trees in equal rows (in terms of the number of trees). Also, he wants to create distinct rows of trees, with only one type of tree in each row.

Find the minimum number of rows required.

The correct option is 22.

To find the minimum number of rows required to plant the trees such that each row contains the same number of trees and only one type of tree, we need to maximize the number of trees in each row. Let this maximum number of trees per row be represented by the Greatest Common Divisor (GCD) of the number of mango, banyan, and banana trees.

The given number of trees are:
Mango trees = 95
Banyan trees = 171
Banana trees = 152

Let's find the prime factorization of each number to determine their GCD:

$$95=5\times 19$$

$$171=3\times 3\times 19=3^2\times 19$$

$$152=2\times 2\times 2\times 19=2^3\times 19$$

The highest common factor (GCD) shared by all three numbers is 19. Therefore, the maximum number of trees in each row is 19.

Now, we calculate the number of rows required for each type of tree:

Number of rows for mango trees:
$$\frac{95}{19}=5$$

Number of rows for banyan trees:
$$\frac{171}{19}=9$$

Number of rows for banana trees:
$$\frac{152}{19}=8$$

Finally, we find the total minimum number of rows by adding the rows of each type of tree together:

Total rows = 5 + 9 + 8 = 22

Thus, the minimum number of rows required is 22.