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?
Answer & explanation
Correct answer: option 4
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