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The average marks obtained by 19 boys of a college is 56. If the highest marks and lowest marks obtained are removed, then the average reduces by 2. What is the average of the highest and lowest marks obtained?

The average marks obtained by 19 boys of a college is 56. If the highest marks and lowest marks obtained are removed, then the average reduces by 2. What is the average of the highest and lowest marks obtained? Correct Answer 73

Short Trick:

Average of 19 boys is 56.

∴ Highest and lowest marks is 56.

⇒ Sum of highest and lowest marks = 56 + 56 = 112

Since average is decreased by 2 when highest and lowest marks are removed.

⇒ Number of boys after removing highest and lowest marks = 19 - 2 = 17

⇒ Actual sum of highest and lowest marks = 112 + 2 × 17 = 112 + 34 = 146

⇒ Average of highest and lowest marks = 146/2 = 73

Detailed Solution:

Total marks obtained by 19 students = 19 × 56 = 1064

Total marks of 17 students after removing highest and lowest marks = 17 × (56 – 2) = 918

Sum of highest and lowest marks = 1064 – 918 = 146

∴ Average of highest and lowest marks = 146 ÷ 2 = 73

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