Question
While solving a mathematical problem, Samidha squared a number and then subtracted 25 from it rather than the required i.e., first subtracting 25 from the number and then squaring it. But she got the right answer. What was the given number ?
Answer: Option A
$$\eqalign{
& {\text{Let the given number be }}x \cr
& {\text{Then,}} \cr
& \Leftrightarrow {x^2} - 25 = {\left( {x - 25} \right)^2}{\text{ }} \cr
& \Leftrightarrow {x^2} - 25 = {x^2} + 625 - 50x \cr
& \Leftrightarrow 50x = 650 \cr
& \Leftrightarrow x = 13 \cr} $$
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$$\eqalign{
& {\text{Let the given number be }}x \cr
& {\text{Then,}} \cr
& \Leftrightarrow {x^2} - 25 = {\left( {x - 25} \right)^2}{\text{ }} \cr
& \Leftrightarrow {x^2} - 25 = {x^2} + 625 - 50x \cr
& \Leftrightarrow 50x = 650 \cr
& \Leftrightarrow x = 13 \cr} $$
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