Question

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 1

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.