Averages Quiz Set 017

We have three equations (p + q)/2 = average of pq, (q + r)/2 = average of qr and (r + p)/2 = average of rp. Adding these three we get p + q + r = (average of pq + average of qr + average of rp) = (38 + 56 + 72) = 166. So p = 166 - (q + r) = 166 - (2 × average of q and r) = 166 - 2 × 56 = 54.

Let the average of all 6 items be x, then the required total is T = 6x. By averages, $x = {5 × 78 + (x + 55)}/6$ which is same as $x × 6 = {5 × 78 + (x + 55)}$, which is same as $T = {5 × 78 + (T/6 + 55)}$, solving for T we get 534 units.

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 = 34, r = 2, n = 16. So increase = $(34 - 2)/16$ = 2.

By the given conditions, A + B = 2 × 16 = 32. Similarly, B + C = 2 × 69 = 138. Adding we get A + 2B + C = 170. We have also been given that A + B + C = 3 × 29 = 87. Subtracting, we get B = 170 - 87 = 83.

The weighted average = ${5 × 144 + 25 × 114}/30$, which equals ${720 + 2850}/30$ = 119.