Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in t...

Question

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A. 6.25
B. 6.5
C. 6.75
D. 7

Answer 1

Solution

Here this problem deals with some of the statistics part and some of the algebraic part, as given in a cricket game, the scored run rate till a particular over is given from which we can calculate the number of runs scored till that particular over. Run rate is the number of runs scored per over. An over has 6 balls. Given the target to be reached in order to win the innings of the cricket match, we have found out the run rate to be scored in the remaining overs.

Complete step-by-step solution:
From the given question we came to know that 10 overs of a cricket match are finished.
Also given the run rate scored in these 10 overs of the cricket match.
$\Rightarrow$ The run rate scored in the first 10 overs = 3.2
Which means that till the first 10 overs the run rate is 3.2, i.e,
In each over scored runs are 3.2 for 10 overs.
$\Rightarrow$ The runs scored in the first 10 overs = $3.2 \times 10$
$\therefore$ The runs scored in the first 10 overs = $32$
The target to be reached is = 282 runs
The no. of remaining overs = 40
$\therefore$ In total there are 50 overs in the cricket match.
The runs scored in the first 10 overs is 32 and the target runs is 282.
$\Rightarrow$ The remaining runs to be scored in the remaining 40 overs to reach the target = $282 - 32$
$\therefore$ The runs to be scored in the 40 overs = $250$
Now we have to calculate the run rate in the 40 overs.
The numbers of runs to be scored in the next 40 overs is 250.
As already discussed the run rate is nothing but the number of runs scored per over.
$\therefore$ The run rate is given by no. of runs per over.
We found out that 250 runs needed from 40 overs.
Now calculating the no. of runs needed per over is given by:
$\Rightarrow \dfrac{{250}}{{40}} = 6.25$
$\Rightarrow$ The no. of runs needed per over in the next 40 overs is 6.25
$\therefore$ The run rate should be 6.25 in order to reach the target.
Option A is the correct answer.

Note: Keep in mind that the run rate is the number of runs scored in an over, where the number of balls an over has is six. Whenever given the target to be reached then to find out the run rate just subtract the no. of runs scored already from the target and divide with the remaining no. of overs to find out the run rate to be scored to reach the target.