### XAT 2012 Question 81

Instructions

The following pie chart shows the percentage distribution of runs scored by a batsman in a test innings.

Question 81

# If 5 of the dot balls had been hit for 4s, and if two of the shots for which the batsman scored 3 runs each had fetched him one run instead, what would have been the central angle of the sector corresponding to the percentage of runs scored in 4s? {Use data from the previous question}

Solution

Net increment in the number of runs due to 5 the dot balls resulting in 4s and two 3s resulting in two 1s = 4*5 - 2*2 = 16.

Therefore, the total number of runs scored by the batsman = 16 + 306 = 322 runs.

The number of runs scored by 4's = 132 + 20 = 152        {We know that batsman scored 132 runs from 4s alone}

The angle subtended by 4's = $$\dfrac{152}{322}\times 360$$ = 169.93 $$\approx$$ 170.