Question

In an orchard there are total 200 trees. If the number of trees in each column is more by 10 than the number of trees in each row, then find the number of trees in each row

Answer 1

Let the number of trees in each row be x.

The number of trees in each column is more by 10 than the number of trees in each row.

∴ The number of trees in each column will be x + 10.

According to the given condition,

There is a total of 200 trees.

∴ x(x + 10) = 200

∴ x² + 10x – 200 = 0

∴ x² + 20x – 10x – 200 = 0

-200

20  -10

20 × (-10) = -200

20 - 10 = 10

∴ x(x + 20) – 10(x + 20) = 0

∴ (x + 20)(x – 10) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

x + 20 = 0 or x – 10 = 0

∴ x = – 20 or x = 10

But, the number of trees cannot be negative.

∴ x = 10

∴ The number of trees in each row is 10.