Question

Study the given information and answer the questions that follow.

Bangalore city corporation is building parks in residential areas across the city. Shown below is one such park. The rectangular park consists of various components like walking track, kids play area, open gym, pond etc.

The caretaker of the park is attempting to plant saplings in the form a square. That is, number of rows of saplings is the same as the number of columns of saplings. On arranging the saplings, he found that $24$ saplings were still left with him. When he increased the number of rows and columns by $1$ , he found that he was short of $25$ saplings.

Find the number of saplings available with him.

Accepted Answer

Given that the caretaker of the park is attempting to plant saplings in the form a square.

That is, number of rows of saplings is the same as the number of columns of saplings.

Let the number of rows and columns initially be $x$ .

On arranging the saplings, he found that $24$ saplings were still left with him.

That means the number of saplings available now are $x^{2} + 24$ .

When he increased the number of rows and columns by $1$ , he found that he was short of $25$ saplings.

That means, the number of saplings available now are ${(x + 1)}^{2} - 25$ .

Let us equate the number of saplings in both the cases and solve the quadratic equation.

$\Rightarrow x^{2} + 24 = {(x + 1)}^{2} - 25$

$\Rightarrow x^{2} + 49 = x^{2} + 2 x + 1$

$\Rightarrow 48 = 2 x$

$\Rightarrow x = 24$ .

That means the total number of saplings are $x^{2} + x = 24^{2} + 24$

$= 600$

Therefore, the total number of saplings available with him are $24$ .

Important Questions on Quadratic Equations

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