Averages Quiz Set 005

Total weight of 18 students is 18 × 29 = 522. Similarly, the total weight of remaining 12 students is 12 × 32 = 384. The total weight of all 30 students is 522 + 384 = 906. So the average = 906/30 = $30{1/5}$.

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula $75 = x/41$, which gives x = $75 × 41 = 3075$. When weight of each of the 41 boys is reduced by 4 Kg, the new total becomes $3075 - 41 × 4 = 2911$, the new average becomes $2911/41 = 71$. TIP: As a shortcut, the new average = old average - error in weighing machine.

By the given conditions, A + B = 2 × 17 = 34. Similarly, B + C = 2 × 43 = 86. Adding we get A + 2B + C = 120. We have also been given that A + B + C = 3 × 31 = 93. Subtracting, we get B = 120 - 93 = 27.

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) = (20 + 48 + 60) = 128. So p = 128 - (q + r) = 128 - (2 × average of q and r) = 128 - 2 × 48 = 32.

The total sale on first six days is 2160 + 2100 + 3234 + 3636 + 1932 + 4266 = 17328. The average for 6 days is: 17328/6, which gives Rs. 2888.