Question

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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.




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Answer 1

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

Answer 2

Answer:

THE NUMBER OF TREES IN EACH ROW BE 10

Step-by-step explanation:

Let the number of tree in each row be x.

Number of trees in each column be x+10

Total number of trees is 200.

x(x+10)=200

x²+10x=200

x²+10x-200=0

x²+20x-10x-200=0

x(x+20)-10(x+20)=0

(x-10)(x+20)=0

x-10=0 (OR). x+20=0

x=10 (OR). x=-20

But the trees cannot be negative so X=-20 is unacceptable and X=10 is acceptable

The number of trees in each row is 10