Question : In a match, the average of runs scored by 7 players is 63. If the runs scored by 6 players are 130, 42, 24, 53, 45, and 54, then how many runs did the 7th player score?
Option 1: 93
Option 2: 90
Option 3: 85
Option 4: 87
Correct Answer: 93
Solution :
Given:
The average runs scored by 7 players = 63
⇒ $\frac{\text{Total runs scored by 7 players}}{7}=63$
The runs scored by 6 players are 130, 42, 24, 53, 45, and 54.
⇒ $\frac{130+42+ 24+ 53+ 45+ 54+x{_7}}{7}=63$ [where $x{_7}$ are the runs scored by 7th player]
⇒ $63\times7=348+x{_7}$
⇒ $348+x{_7}=441$
⇒ $x{_7}=441-348=93$
Hence, the correct answer is 93.
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