Question

In garden there are some rows and columns. The number of trees in a row is greater than that in each column by 10. Find the number of trees in each row if the total number of trees are 200.

Answer 1

Let the number of trees in each column of the garden be x.
Then, the number of trees in each row of the garden will be (x + 10).
Thus, we get:
x(x + 10) = 200
$\Rightarrow$x² + 10x = 200
$\Rightarrow$x² + 10x – 200 = 0
On splitting the middle term 10x as 20x – 10x, we get:
x² + 20x – 10x – 200 = 0
$\Rightarrow$x(x + 20) – 10(x + 20) = 0
$\Rightarrow$ (x + 20)(x – 10) = 0
$\Rightarrow$x + 20 = 0 or x – 10 = 0
$\Rightarrow$ x = –20 or x = 10
Since, x is the number of trees in each column of the garden, it cannot be negative.
Thus, x = 10 and x + 10 = 10 + 10 = 20.
Therefore, the number of trees in each row of the garden is 20.