The square of a positive number is 2000% greater than the number itself, then the square of that number is :a)1762b)1635c)441d)139Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Problem:
The square of a positive number is 2000% greater than the number itself. Find the square of that number.

Solution:
Let's assume the positive number as 'x'.

Step 1: Write the given information as an equation.
The square of the number is 2000% greater than the number itself, which can be expressed as:
x^2 = x + (2000/100)x

Simplifying the equation, we get:
x^2 = x + 20x

Step 2: Combine like terms.
x^2 = 21x

Step 3: Move all terms to one side to set the equation equal to zero.
x^2 - 21x = 0

Step 4: Factor out the common factor, 'x'.
x(x - 21) = 0

Step 5: Solve for 'x'.
Setting each factor equal to zero, we get:
x = 0 or x - 21 = 0

For a positive number, x cannot be equal to zero. Therefore, we take the other solution:
x - 21 = 0
x = 21

Step 6: Find the square of the number.
x^2 = 21^2
x^2 = 441

Conclusion:
The square of the positive number is 441, which is option 'C'.

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