The batting average of a cricket player for 30 innings is 40 runs. His highest score exceeds his lowest score by 100 runs. If these two innings are not included, the average of the remaining 28 innings is 38 runs. The lowest score of the player is

Batting average of the cricket player for 30 innings = 40 runs

=> Total runs in 30 innings = $$40\times30=1200$$

Average of 28 innings = 38

=> Total runs in 28 innings = $$38\times28=1064$$

Let highest score = $$x$$ and lowest score = $$y$$

Now, sum of highest and lowest score = $$x+y=(1200-1064)=136$$ --------------(i)

According to ques, => $$x-y=100$$ --------------(ii)

Subtracting equation (ii) from (i),

=> $$2y=136-100=36$$

=> $$y=\frac{36}{2}=18$$ runs

=> Ans - (A)