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.

Answer 1

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.
$$\begin{gathered} 5\left(x+10\right)=x^2 \\ \Rightarrow 5x+50=x^2 \\ \Rightarrow x^2-5x-50=0 \\ \Rightarrow x^2-10x+5x-50=0 \\ \Rightarrow x\left(x-10\right)+5\left(x-10\right)=0 \\ \Rightarrow \left(x+5\right)\left(x-10\right)=0 \\ \Rightarrow x=10,-5 \end{gathered}$$
The score is not negative so, Suyash scored 10 marks in first test.