Averages Quiz Set 004

The total sale on first five days is 2262 + 666 + 1740 + 3216 + 4926 = 12810. Let the sale on 6th day be x. The average for 6 days is: 2281 = ${12810 + x}/6$ which gives x = $6 × 2281 - 12810$ = Rs. 876.

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 13 terms as 203. So a + 13 - 1 = 203, which gives a = 191. The average of first 57 terms would be a + 57 - 1 = 191 + 57 - 1 = 247.

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 = 85, r = 5, n = 10. So increase = $(85 - 5)/10$ = 8.

The sum of first n natural numbers is $(n × (n + 1))/2$. The average is ${(n × (n + 1))/2}/n$ which is $(n + 1)/2.$ Putting n = 343, we get average = 172.

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula $28 = x/44$, which gives x = $28 × 44 = 1232$. When weight of each of the 44 boys is reduced by 2 Kg, the new total becomes $1232 - 44 × 2 = 1144$, the new average becomes $1144/44 = 26$. TIP: As a shortcut, the new average = old average - error in weighing machine.