In the orange garden of Mr. Madhusudan there are 150 orange trees. The

1.	In the orange garden of Mr. Madhusudan there are 150 orange trees. The number of trees in each row is 5 more than that in each column. Find the number of trees in each row and each column with the help of following flow chart.
Answer» i. Number of trees in a column is x. ii. Number of trees in a row = x + 5 iii. Total number of trees = x x (x + 5) iv. According to the given condition, x(x + 5) = 150 ∴ x² + 5x = 150 ∴ x² + 5x – 150 = 0 v. x² + 15x – 10x – 150 = 0 ∴ x(x+ 15) – 10(x + 15) = 0 ∴ (x + 15)(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 + 15 = 0 or x – 10 = 0 ∴ x = -15 or x = 10 But, number of trees cannot be negative. ∴ x = 10 vi. Number of trees in a column is 10. vii. Number of trees in a row = x + 5 = 10 + 5 = 15 ∴ Number of trees in a row is 15.

In the orange garden of Mr. Madhusudan there are 150 orange trees. The number of trees in each row is 5 more than that in each column. Find the number of trees in each row and each column with the help of following flow chart.

Answer»

i. Number of trees in a column is x.

ii. Number of trees in a row = x + 5

iii. Total number of trees = x x (x + 5)

iv. According to the given condition,

x(x + 5) = 150

∴ x² + 5x = 150

∴ x² + 5x – 150 = 0

v. x² + 15x – 10x – 150 = 0

∴ x(x+ 15) – 10(x + 15) = 0

∴ (x + 15)(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 + 15 = 0 or x – 10 = 0

∴ x = -15 or x = 10

But, number of trees cannot be negative.

∴ x = 10

vi. Number of trees in a column is 10.

vii. Number of trees in a row = x + 5 = 10 + 5 = 15

∴ Number of trees in a row is 15.