Averages Quiz Set 003

The total increase of weight = 11 × 14 = 154. So the weight of the new bogie = 13 + 154 = 167 Kg.

Let the wage of a man and a woman be x and x - 5. We are given the average ${x × 412 + (x - 5) × 103}/{412 + 103}$ = 194. This equation can be solved for x to get Rs. 195 as the answer.

Let the annual spending be Rs. M. The catch in this question is that the spending remains fixed, so the consumption varies from year to year. We shall calculate the total consumption first. Let r1, r2 and r3 be the rates for the three successive years. Consumption in first year = M/r1. Similarly, we get M/r2 and M/r3. So total consumption is $M/{r1} + M/{r2} + M/{r3}$. Money spent in three years is 3M. So the required average = ${3M}/{M/{r1} + M/{r2} + M/{r3}}$ which simplifies to ${3r1r2r3}/{r1r2 + r2r3 + r3r1}$. Putting r1 = 10, r2 = 14, r3 = 16, we get $12{108/131}$. You might be wondering why I derived the formula first. The reason is that sometimes it is better to postpone calculations till the end.

By the given conditions, A + B = 2 × 14 = 28. Similarly, B + C = 2 × 37 = 74. Adding we get A + 2B + C = 102. We have also been given that A + B + C = 3 × 26 = 78. Subtracting, we get B = 102 - 78 = 24.

Total weight of 17 students is 17 × 27 = 459. Similarly, the total weight of remaining 16 students is 16 × 33 = 528. The total weight of all 33 students is 459 + 528 = 987. So the average = 987/33 = $29{10/11}$.