Question

Sachin has a batting average of 99 in 80 innings. He was out for duck in his 80th innings.If he were to have a batting average of 100 how much should have been scored by him in his 80th match?
A) 80
B) 180
C) 99
D) 100 ​

Answer 1

Given:

• Average = 99, in 80 innings

• Runs scored in 80th innings = 0

To find:

Runs scored in the 80th innings, if the average is 100

Solution:

$\sf{\frac{x_{1}+x_{2}+x_{3}..+x_{80}}{80} = 99}$

We're given that $\sf{x_{80} = 0}$

→ $\sf{\frac{x_{1}+x_{2}+x_{3}..+x_{79}}{80} = 99}$

→ $\sf{x_{1}+x_{2}+x_{3}..+x_{79} = 99 \times 80}$

→ $\sf{x_{1}+x_{2}+x_{3}..+x_{79}= 720}$ __(1)

Now, if we keep $\sf{x_{80} = x}$ and the average as 100, we get:

→ $\sf{\frac{x_{1}+x_{2}+x_{3}..+x_{79} +x_{80}}{80} = 100}$

→ $\sf{ 720 + x = 800}$ (Put (1))

→ $\sf{x = 80}$

$\boxed{\sf{\red{Option\: A\: is\: right}}}$