Averages Quiz Set 002

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula $46 = x/25$, which gives x = $46 × 25 = 1150$. When weight of each of the 25 boys is reduced by 3 Kg, the new total becomes $1150 - 25 × 3 = 1075$, the new average becomes $1075/25 = 43$. TIP: As a shortcut, the new average = old average - error in weighing machine.

Total weight of 13 students is 13 × 39 = 507. Similarly, the total weight of remaining 17 students is 17 × 30 = 510. The total weight of all 30 students is 507 + 510 = 1017. So the average = 1017/30 = $33{9/10}$.

Let the present ages of the three friends be a, b and c. We are given ${(b - 5) + (c - 5)}/2$ = 13. Which gives b + c = 36. We are also given ${(a - 3) + (b - 3) + (c - 3)}/3$ = 30, which gives a + b + c = 3 * 30 + 9 = 99. Putting b + c here we get a = 99 - (b + c) = 99 - 36 = 63 years.

The total sale on first five days is 4392 + 5040 + 3630 + 1554 + 612 = 15228. Let the sale on 6th day be x. The average for 6 days is: 3179 = ${15228 + x}/6$ which gives x = $6 × 3179 - 15228$ = Rs. 3846.

Let the average of all 6 boys be x, then the required total is T = 6x. By averages, $x = {5 × 60 + (x + 55)}/6$ which is same as $x × 6 = {5 × 60 + (x + 55)}$, which is same as $T = {5 × 60 + (T/6 + 55)}$, solving for T we get 426 Kg.