While solving a mathematical problem, Atul squared the initial number and then subtracted 15 from it. Pratul first subtracted 15 from the initial number and then squared the difference. If both obtained the same answer, what was the initial number?

Correct option is A

Given:

Atul squared the initial number and then subtracted 15 from it.

Pratul first subtracted 15 from the initial number and then squared the difference.

Solution:

Let initial number is x .

Atul squared the initial number and then subtracted 15 :

Atul’s result =  $$x^2- 15$$ 

Pratul first subtracted 15 from the initial number and then squared the result:

Pratul’s result = $$(x-15)^2$$ 

Now:

​$$x ^2 −15=(x−15) ^2$$ 

$$x ^2 −15=x ^2 −30x+225$$ 

​$$−15=−30x+225$$

​​$$−15−225=−30x$$ 

​$$−240=−30x$$

$$x = \frac{-240}{-30} = 8$$

Thus the initial number is 8. 

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xx^2
x=−240−30=8x = \frac{-240}{-30} = 8x=−30−240​=8​​