Question

A batsman has a certain average of runs for 16 innings, in the $17^{th}$ inning, he makes a score of 85 runs thereby increasing his average by 3. What is the average of 17 innings?

Answer 1

Hint: To solve this question first we will figure out how many runs does batsman made in 16 innings by letting it’s average equals to A. similarly, we will find out the average of 17 innings in terms of A and run scored in 17 innings also, then by using concept of average value, we will determine the values of A. finally on substitution of value of A we get average of batsman in 17 innings.

Complete step by step answer:
Before we solve this question, let us see what the meaning of Average is.
Average of numbers is the number you get when you add two or more numbers and then divide the sum by the total number of figures you added.
Let us consider n – items say, ${{n}_{1}},{{n}_{2}},{{n}_{3}},........,{{n}_{n}}$ , then the average of these n – items will be $\bar{x}=\dfrac{{{n}_{1}}+{{n}_{2}}+........+{{n}_{n}}}{n}$ , where $\bar{x}$ denotes average value.

Now, in question it is given that a batsman has a certain average of runs for 16 innings. So let the average of batsman for 16 innings be A.
As in question it is given that in 17 innings he makes a score of 85 runs thereby increasing his average by 3.
Then, the average of runs for 17 innings will be equal to A + 3.
Also, we can say that total runs made by batsman in 16 innings will be equal to its average in 16 innings multiplied by 16.
So, Total runs for 16 innings = 16A
Now, as batsman in 17 innings he makes a score of 85 runs.
So, total run of batsman till 17 innings will be 16A + 85
As, it is given that in 17 innings he makes a score of 85 runs thereby increasing his average by 3.
Then, $\dfrac{16A+85}{17}=A+3$ , where 17 is total number of innings, 16A + 85 is total score till 17 innings and A + 3 is average of 17 innings.
On solving, we get
$16A+85=17(A+3)$
$16A+85=17A+51$
A = 34

So, average of 17 inning will be 34 + 3 = 37 runs

Note: To solve such these types of question, one must know the concept of Average Value, which is, if we have n – items say, ${{n}_{1}},{{n}_{2}},{{n}_{3}},........,{{n}_{n}}$ , then the average of these n – items will be $\bar{x}=\dfrac{{{n}_{1}}+{{n}_{2}}+........+{{n}_{n}}}{n}$. Try to avoid calculation mistakes as it will affect the final answer of the solution.