Question 24.
In which of these pairs of over numbers, the team could have scored 22 runs in total?
Question Explanation
It is given that the runs in any over is an integer. So, the run rate multiplied by overs should give us an integer.
1 ≤ N - 2 < N + 6 ≤ 20
The range of N is [3, 14].
After N overs, the run rate is given as 7.43. So, 7.43*N has to be an integer. Let's try putting all the possible values N and see where we get an integer.
3*7.43=22.29
4*7.43=29.72
5*7.43=36.15
6*7.43=44.58
7*7.43=52.01
Here, we got an integer; since the run rate is reduced to 2 decimal points, We can not get an exact integer.
So, N can be 7. Let's also check the remaining possible values of N.
8*7.43=59.44
9*7.43=66.87
10*7.43=74.3
11*7.43=81.73
12*7.43= 89.16
13*7.43=96.59
14*7.43=102.02
N can also be 14.
If N=14, the (N+2)*8.11=16*8.11 should also be an integer. But it is 129.76. So, N is not 14. The only possible value is 7.
N-2 --- 8.0 = 5*8=40
N --- 7.43 = 52.01
N+2 --- 8.11 = 9*8.11=72.99
N+4--- 8.45 = 11*8.45 = 92.95
N+6 --- 8.08 = 13*8.08= 105.04
Every number is almost an integer, so N will be 7.
Now, let's calculate the runs scored in each of these overs.
After five overs, the score is 40
After seven overs, the score is 52
So, the sum of scores in 6 and 7 overs is 12. They have to score a minimum of 6 in an over. So, 6 is the sixth over, and 6 in the seventh over.
After the 9th over, the score was 73. They scored 21 in the 8th and 9th over.
After the 11th over, the score was 93; they scored 20 in the 10th and 11th.
After the 13th over, the score was 105; they scored 12 in the 12th and 13th over.
Option A) The sum of scores in 6 and 7 overs is 12.
Option B) The maximum score possible in the 7th and 8th overs is 21 because we know that 6 runs were scored in the 7th over, and the maximum possible score in the 8th over is 15, which makes the sum 21, and it is not sufficient to score 22 runs in the 7th and 8th overs.
Option C) The sum of scores in 8 and 9 overs is 21.
Option D) The sum of scores in the 9 and 10 overs cannot be determined uniquely from the information given, but we know that in the 8 and 9 overs, they scored 21 runs, and in the 10th and 11th overs, they scored 20 runs. So, them scoring 22 runs in 9th and 10th overs is numerically possible and this is the correct option.
Option E) The sum of scores in 10 and 11 overs is 20.
So, only option D could be the answer.
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