Question

How many runs does a cricketer should make in his next inning so as to raise his average to $24$. If his current average is $21.5$ runs, he played $10$ complete innings. Choose the correct option.
(A) $44$
(B) $49$
(C) $45$
(D) $50$

Answer 1

Hint:As we have to find runs made by the cricketer in his next inning first we calculate the total runs he scored in $10$ innings i.e. multiply average runs and total inning. We consider runs in his next inning as ‘a’. Then we will find the average of runs including his next inning as well we get it by adding runs of $10$ inning, ‘a’ and divide the sum by $11$ which should be equal to $24$. By solving the equation we get the value of runs in the innings.

Complete step-by-step answer:
According to the question we have to find the number of runs in his $11$th innings. Let us take it as ‘a’.
It is given that
(i) Total number of innings is $10$,
(ii) average runs in $10$ innings is $21.5$,
(iii) average of $11$ innings is $24$
Now,
Total numbers of runs in $10$ innings = $(average{\text{ }}runs \times total{\text{ }}inning)$
We get, =$(21.5 \times 10)$
              $ = 215$
Average in $11$ innings =\[(\dfrac{{Total{\text{ }}runs{\text{ }}of{\text{ }}10{\text{ }}inning + Runs{\text{ }}in{\text{ }}{{11}^{th}}inning}}{{Total{\text{ }}number{\text{ }}of{\text{ }}innings}})\]
Now we put all the values in the formula, we get
$ \Rightarrow (\dfrac{{215 + a}}{{11}}) = 24$
Now, by taking $11$ to R.H.S we get,
$ \Rightarrow 215 + a = 24 \times 11$
Now, by multiplying $24 \times 11$in R.H.S we get,
$ \Rightarrow 215 + a = 264$
Now, by taking 215 to R.H.S we get,
$ \Rightarrow a = 264 - 215$
Subtracting $264 - 215$, we get
$ \Rightarrow a = 49$
So, the number of runs in his $11$th innings=$49$ runs.

So, the correct answer is “Option B”.

Note:Alternative Method: First we prepare equation then we put all the values
Let us consider:
 Average to be raised is ‘y’=$24$
Completed innings be ‘n’=$10$
His average runs in ‘n’ inning be x=$21.5$
Required number of runs he will make in next innings be $n(y - x) + y$
Now we put all the values in the equation $n(y - x) + y$, we get,
$ \Rightarrow Required{\text{ }}runs = 10(24 - 21.5) + 24$
Now we subtracting $24 - 21.5$, we get,
                   $ \Rightarrow Required{\text{ }}runs = 10 \times 2.5 + 24$
Now, by multiplying $10 \times 2.5$,we get
                  $ \Rightarrow Required{\text{ }}runs = 25 + 24$
Now we add $25 + 24$, we get,
          $ \Rightarrow Required{\text{ }}runs = 49$
$\therefore $ Required Runs are $49$.