In a cricket match an over contains six balls. In a T-20 Cricket match it was already 5 balls bowled in the last over. If Sachin hits six for the last ball the mean becomes 4 runs per ball in the over. But Sachin hits four runs. Then the mean score per ball in that over is
A) 3
B) \(3\frac{2}{3}\)
C) 4
D) 6
Correct option is (B) 3 2/3
Let sum of scored runs on first 5 balls in the last over is x.
After hitting 6 on last ball of the over, the mean score becomes 4 runs per ball.
\(\therefore\) \(\frac{x+6}6=4\)
\(\Rightarrow\) \(\frac{x}6+1=4\)
\(\Rightarrow\) \(\frac{x}6=4-1=3\)
\(\Rightarrow\) x = 6 \(\times\) 3 = 18
Hence, the sum of scored runs on first 5 balls in the last over is 18.
Given that Sachin scored 4 runs on last ball.
\(\therefore\) Mean \(=\frac{18+4}6\)
\(=\frac{22}6\) \(=3\frac46\)
\(=3\frac23\)
Hence, the mean score per ball in that over is \(3\frac23.\)