Question : The bar graph below gives the runs scored by Team A in the first six overs of a cricket match.
The runs scored by Team A in the 7th over was 5 more than the runs scored by them in the 8th over, but 6 less than the runs scored by them in the 9th over. If the average runs scored per over by Team A in the first nine overs of the match was 9, how many runs did the team score in the 8th over?
Option 1: 5
Option 2: 7
Option 3: 6
Option 4: 8
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Correct Answer: 6
Solution :
Total runs in 6 overs = 4 + 15 + 8 + 7 + 10 + 3 = 47
Let the total runs scored in the 7th over be $x$.
⇒ Runs scored in the 8th over = $x$ – 5
And, Runs scored in the 9th over = $x$ + 6
Given the average runs scored till the 9th over = 9
⇒ $\frac{\text{Total runs scored till the 9th over}}{9}=9$
⇒ Total runs scored till the 9th over = 9$\times$9 = 81
⇒ 47 + $x$ + $x$ – 5 + $x$ + 6 = 81
⇒ 48 + 3$x$ = 81
⇒ 3$x$ = 81 – 48
⇒ 3$x$ = 33
⇒ $x$ = 11
⇒ Runs scored in the 8th over = 11 – 5 = 6
Hence, the correct answer is 6.
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