Question

The average of $20$ numbers is zero . Of them , at the most , how many may be greater than zero ?
A - $0$
B - $1$
C - $10$
D - $19$

Answer 1

Hint: As we know that the average equal to ${\displaystyle \frac{\text{Sum of the number }}{\text{Total number of number }}}$ in question it equal to $0$ . So from here Sum of numbers is equal to $0$ , hence this is possible as sum of $12$ number is $c$ and rest $8$ number sum is $-c$ then sum of $20$ number is $0$ in the question we have the maximum positive number possible .

Complete step-by-step answer:
In this question we have to find out at the most , how many may be greater than zero if the average of $20$ numbers is zero .
So average is equal to = ${\displaystyle \frac{\text{Sum of the number }}{\text{Total number of number }}}$
In this question it is given that the average of $20$ numbers is zero
${\displaystyle \frac{\text{Sum of the number }}{\text{Total number of number }}}$ = $0$
Hence it mean that the Sum of the numbers = $0$
So in the question it is given we have to find out the at most positive value mean maximum positive number possible .
As if the sum of $19$ positive numbers is equal to the $a$ and there is $20$ number whose value equal to the negative of the $a$ hence total sum is equal to $0$ ,
And the Average of the Numbers is equal to the $0$ .
So the maximum positive value possible is the $19$ and option D is the correct answer .

Note: The average formula has many applications both in real-life. Suppose if we have to find the average age of men or women in a group or average male height in India, then we calculate it by adding all the values and dividing it by the number of values.