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प्रश्न
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
उत्तर
Let the number of trees in each row be x.
The number of trees in each column is more by 10 than the number of trees in each row.
∴ The number of trees in each column will be x + 10.
According to the given condition,
There is a total of 200 trees.
∴ x(x + 10) = 200
∴ x2 + 10x – 200 = 0
∴ x2 + 20x – 10x – 200 = 0
| -200 |
| 20 -10 |
| 20 × (-10) = -200 |
| 20 - 10 = 10 |
∴ x(x + 20) – 10(x + 20) = 0
∴ (x + 20)(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 + 20 = 0 or x – 10 = 0
∴ x = – 20 or x = 10
But, the number of trees cannot be negative.
∴ x = 10
∴ The number of trees in each row is 10.
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