A batsman makes a score of 270 runs in the 87 | vedclass

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(D) Let the average after $86$ innings be $A$. The total runs after $86$ innings is $86A$.In the $87^{th}$ inning,he scores $270$ runs,so the new tota

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(D) Let the average after $86$ innings be $A$. The total runs after $86$ innings is $86A$.In the $87^{th}$ inning,he scores $270$ runs,so the new total is $86A + 270$.The new average is $\frac{86A + 270}{87} = A + x$,where $x$ is a whole number.$86A + 270 = 87A + 87x$$270 - 87x = A$Since $A$ must be positive,$270 - 87x > 0$,so $87x If $x = 0$,$A = 270$,new average $= 270 + 0 = 270$.If $x = 1$,$A = 270 - 87 = 183$,new average $= 183 + 1 = 184$.If $x = 2$,$A = 270 - 174 = 96$,new average $= 96 + 2 = 98$.If $x = 3$,$A = 270 - 261 = 9$,new average $= 9 + 3 = 12$.Thus,the possible values for the new average are $12, 98, 184, 270$.

$A$ batsman makes a score of $270$ runs in the $87^{th}$ inning and thus increases his average by a certain number of runs that is a whole number. Find the possible values of the new average.

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