The average marks scored by Ajay in certain number of tests is 84. He scored 100 marks in his last test. If his average score of all these tests is 86, then the total number of tests he appeared is ____.

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Solution

The correct option is A 8
Let 'x' denote the certain number of tests taken by Ajay.
$x_{1} + x_{2} + x_{3} + \dots \dots x_{n} = 84 x$ ---(i)

In the last test he scored 100 marks and his average score becomes 86.
Now, the total number of tests he appeared is 'x + 1'.
$\frac{x_{1} + x_{2} + x_{3} + \dots \dots x_{n} + 100}{x + 1} = 86$
Substituting the value of equation (i) in the above equation, we get
$\frac{84 x + 100}{x + 1} = 86$
$x = 7$

Hence, the total number of tests he appeared = x + 1 = 7 + 1 = 8.

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