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Question
Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.
Solution
Let the score in the first test be x.
Suyash's score in second test is 10 more than that in the first.
So, his score in the second test = x + 10
5 times the score of the second test is the same as square of the score in the first test.
\[5\left( x + 10 \right) = x^2 \]
\[ \Rightarrow 5x + 50 = x^2 \]
\[ \Rightarrow x^2 - 5x - 50 = 0\]
\[ \Rightarrow x^2 - 10x + 5x - 50 = 0\]
\[ \Rightarrow x\left( x - 10 \right) + 5\left( x - 10 \right) = 0\]
\[ \Rightarrow \left( x + 5 \right)\left( x - 10 \right) = 0\]
\[ \Rightarrow x = 10, - 5\]
The score is not negative so, Suyash scored 10 marks in first test.
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