A forester wants to plant 44 apple trees, 66 banana trees, and 110 mango trees in equal rows. Also, he wants to make distinct rows of different trees. The number of minimum rows that are required are:

• (a) 2
• (b) 3
• (c) 10
• (d) 11

To determine the minimum number of rows needed for planting the trees, we first need to find the greatest common divisor (GCD) of the numbers of each type of tree: 44 apple trees, 66 banana trees, and 110 mango trees.

Finding the GCD

The GCD is the largest number that can evenly divide all three quantities. Let's break down each number into its prime factors:

• 44 = 2 × 2 × 11
• 66 = 2 × 3 × 11
• 110 = 2 × 5 × 11

Identifying Common Factors

The common factors among these numbers are:

• 2
• 11

The GCD is the product of the common factors:

GCD = 2 × 11 = 22

Calculating the Number of Rows

Now, to find the number of rows, we divide each quantity of trees by the GCD:

• 44 ÷ 22 = 2 rows of apple trees
• 66 ÷ 22 = 3 rows of banana trees
• 110 ÷ 22 = 5 rows of mango trees

Summing Up the Rows

Adding these together gives:

Total rows = 2 + 3 + 5 = 10

Thus, the minimum number of distinct rows required is 10.

Final Answer

The correct option is (c) 10.