Question

The ratio of numbers of runs scored by Virat in 1st and 2nd match was 11:15. In the 3rd match
he scored 50% more than that of 1st match, and the average runs of 3 matches became 170
What was average runs scored by Virat in 1st and 3rd match?

Answer 1

Ratio of runs scored in 1st and 2nd innings is $11:15$.

Let runs scored in 1st innings be $11x$ and runs scored in 2nd innings be $15x$.

Now, it is given that in 3rd innings, virat scored 50% more runs than runs scored in 1st innings.

$\text{Runs scored in 3rd innings = }11x + \dfrac{1}{2} \times 11x\\\Rightarrow 16.5x$

We are provided that the average of 3 innings becomes 170.

Using the formula of average

$Average = \dfrac{\text{Sum of all observations}}{\text{Count of observations}}$

$170 = \dfrac {11x + 15x + 16.5x}{3}\\\Rightarrow \dfrac{42.5x }{3} =170\\\Rightarrow x = 12$

Sum of runs scored in 1st and 3rd innings is $11x + 16.5x = 27.5x$

Putting the value of x $\Rightarrow 27.5 \times 12$

$\text{Average of 1st and 3rd innings runs} =\dfrac{\text{Runs scored in 1st innings + Runs scored in 3rd innings}}{2}$

$\Rightarrow \dfrac {27.5 \times 12}{2}\\\Rightarrow 27.5 \times 6\\\Rightarrow 165$

Hence, average of runs scored in 1st and 3rd innings is 165.