Average marks obtained by 19 boys of a college is 48. If the highest and lowest marks obtained are removed, then the average reduces by 4. What is the average of the highest and lowest marks obtained?

82

Average of marks obtained by 19 boys = $\frac{Sum\;of\;their\;marks}{19}$

⇒  $\frac{Sum\;of\;their\;marks}{19}$ = 48

⇒ Sum of their marks = 19 x 48 = 912

Let the highest and the lowest marks be x and y, respectively

⇒ x + Sum of marks of 17 boys + y = 912

When x and y are removed from the sum, the average becomes 44

⇒ $\frac{Sum\;of\;marks\;of\;17\;boys}{17}$ = 44

⇒ Sum of marks of 17 boys = 44 x 17 = 748

⇒ Then, x + y = Sum of marks of 19 boys - Sum of marks of 17 boys 

⇒          x + y = 912 - 748 = 164

Average of x and y = $\frac{x+y}{2}$ = $\frac{164}{2}$

                            = 82