Discussion
The average score of a batsman after his 90th innings was 79.2. After 120th innings, his average score increased by 7.8. What is his average score in the last 30 innings?
Answer: C
His average in the last 30 innings is 110.4.
The new average after 120 innings is \(79.2 + 7.8 = 87\).
\[ \begin{aligned} 120 \times 87 &= 10440 \\ 90 \times 79.2 &= 7128 \\ \frac{10440 - 7128}{30} &= \frac{3312}{30} = 110.4 \end{aligned} \]
A quick check: the extra 30 innings raised the average of 120 by 7.8, so they exceeded the old average by \(7.8 \times 120 / 30 = 31.2\), and \(79.2 + 31.2 = 110.4\). 65.1 would have lowered the average, and 137.7 or 157.1 would have raised it by far more than 7.8.
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