Question

M.S. Dhoni has a certain batting average N ( a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs, which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?

Answer 1

Let the Total runs scored by M.S. Dhoni in 86 innings be x
Then,
$\frac{x}{86} = N$

x = 86×N

After the 87th innings, Let the average be increased by K units,

then,
$\frac{x+270}{87}= N+ K$

Putting x= 86N
we get,
86N + 270 = 87(N+K)

Solving, we get,
$K= \frac{270-N}{87}$

So, we get 3 possible whole number values of K.