Averages Quiz Set 013

Let the present ages of the three friends be a, b and c. We are given ${(b - 5) + (c - 5)}/2$ = 19. Which gives b + c = 48. We are also given ${(a - 3) + (b - 3) + (c - 3)}/3$ = 31, which gives a + b + c = 3 * 31 + 9 = 102. Putting b + c here we get a = 102 - (b + c) = 102 - 48 = 54 years.

The total increase of weight = 12 × 9 = 108. So the weight of the new bogie = 12 + 108 = 120 Kg.

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 = 263, we get average = 132.

Let the average of all 5 bulbs be x, then the required total is T = 5x. By averages, $x = {4 × 81 + (x + 44)}/5$ which is same as $x × 5 = {4 × 81 + (x + 44)}$, which is same as $T = {4 × 81 + (T/5 + 44)}$, solving for T we get 460 years.

The total sale on first five days is 1770 + 1086 + 2220 + 3774 + 2154 = 11004. Let the sale on 6th day be x. The average for 6 days is: 1966 = ${11004 + x}/6$ which gives x = $6 × 1966 - 11004$ = Rs. 792.