Question : A batsman scores 87 runs in the 21st match of his career. His average runs per match increases by 2. What was his average before the 21st match?
Option 1: 45
Option 2: 46
Option 3: 44
Option 4: 43
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Correct Answer: 45
Solution :
Let his average before the 21
st
match be $x$.
New average after 21
st
match = $(x + 2)$
Total runs before the 21
st
match = $20x$
Runs scored in the 21
st
match = 87
⇒ $x + 2$ = $\frac{87 + 20x}{21}$
⇒ $21x + 42$ = $87 + 20x$
⇒ $x$ = $45$
Hence, the correct answer is 45.
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