Question

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

• A. $8$
• B. $7$
• C. $9$
• D. $10$

Answer 1

The correct option is A

$8$

Step 1: Given data

As per data given in the question,

We have,

The average marks scored by Ajay in certain number of tests is $84$.

Mark scored in last test $=100$

New average $=86$

Step 2: Concept of average

As the average mark scored by Ajay in certain number of test is $84$.

So, let the number of tests $=n$

So, $x_1+x_2+x_3+\dots x_n=84x------\left(i\right)$

Step 3: Calculation of “x”

After scoring $100$ marks in last test his average becomes $86$.

So,

$$\begin{gathered} \frac{84x+100}{x+1}=86 \\ \Rightarrow 84x+100=86x+86 \\ \Rightarrow 2x=14 \\ \Rightarrow x=7 \end{gathered}$$

Total number of test$7+1=8$

Hence, option (a) is the correct choice.