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

Step-by-step explanation:

Let there be m rows and n columns.

Since, number of trees in rows is greater than columns by 10

thus, n−m=10 or m=n−10

nm=200

n(n−10)=200

${n}^{2} - 10n - 200 = 0$

$n = \frac{10 + \sqrt{100 + 800} }{2} \\ n = \frac{10 + 30}{2}$

n=20,−10

Neglect the negative value, number of rows =20

Answer 2

ANSWER:

Given:

• Total of 200 trees

• No. of trees in each column is 10 more than in each row.

To Find:

• Number of trees in each row.

Solution:

Let the no. of trees in each row be x. -----(1)

So,

⇒ No. of trees in each column = x + 10 -----(2)

And,

⇒ Total trees = (no. of trees in each row) × (no. of trees in each column)

Placing values from (1) & (2)

⇒ 200 = (x) × (x + 10)

⇒ 200 = x² + 10x

Transposing RHS to LHS,

⇒ 0 = x² + 10x - 200

⇒ x² + 10x - 200 = 0

Splitting the middle term,

⇒ x² + 20x - 10x - 200 = 0

Taking out commons,

⇒ x(x + 20) - 10(x + 20) = 0

⇒ (x - 10)(x + 20) = 0

⇒ x = 10 or -20.

As no. of trees cant be negative, x≠-20.

So,

⇒ No. of trees in each row = 10

Hence, total no of trees in each row is 10.

No. of trees in each column = 10 + 10 = 20