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## Explanation

- Twenty times a positive integer is less than its square by 96.

The integer can be figure out in this way.

Let suppose the integer is y.

20 times of y and its square

20y & y^{2}

20 times of y is less than its square by 96

20y + 96 = y^{2} ________ (i)

Through equation (i) we can easily find out the value of y (y = 24).

## To Find

Number = ?

## Solution

Let suppose

Number = y

According to the given condition

20y + 96 = y^{2}

y^{2 }– 20y – 96 = 0

y^{2 }– 24y + 4y – 96 = 0

y(y – 24) + 4(y – 24) = 0

(y – 24)(y + 4) = 0

y – 24 = 0 or y + 4 = 0

y = 24 (possible) or y = -4 (not possible)

**Required Number = 24 answer**

## Conclusion

Twenty times a positive integer is less than its square by 96. The required integer will be 24.