Averages Quiz Set 008

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is ${a + (a + (n-1) × 2)}/2$ which is = a + n-1. We are given the average of first 29 terms as 137. So a + 29 - 1 = 137, which gives a = 109. The average of first 64 terms would be a + 64 - 1 = 109 + 64 - 1 = 172.

Let the total score of the class before grace marks be x. Then, by average formula $80 = x/8$, which gives x = $80 × 8 = 640$. When grace marks = 8 are added for each of the 8 students, the new total becomes $640 + 8 × 8 = 704$, the new average becomes $704/8 = 88$. TIP: As a shortcut, the new average = old average + grace marks.

If a number r is replaced by a number R, the increase/decrease of average is determined according to the formula $(R - r)/n$. So in our case we have R = 232, r = 11, n = 17. So increase = $(232 - 11)/17$ = 13.

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is ${a + (a + (n-1) × 2)}/2$ which is = a + n-1. We are given the average of first 22 terms as 72. So a + 22 - 1 = 72, which gives a = 51. The average of first 79 terms would be a + 79 - 1 = 51 + 79 - 1 = 129.

The total sale on first five days is 1308 + 2706 + 2280 + 2898 + 2796 = 11988. Let the sale on 6th day be x. The average for 6 days is: 2684 = ${11988 + x}/6$ which gives x = $6 × 2684 - 11988$ = Rs. 4116.