Averages Quiz Set 014

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 = 112, r = 13, n = 11. So increase = $(112 - 13)/11$ = 9.

The sums of the weights of all the students is 30 × 6 + 40 × 3 + 40 × 4 = 460. The required average = 460/total students = $460/{30 + 40 + 40}$ = ${46/11}$, which is same as: $4{2/11}$.

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 = 152, r = 12, n = 14. So increase = $(152 - 12)/14$ = 10.

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 = 12, r2 = 6, r3 = 2, we get 4. You might be wondering why I derived the formula first. The reason is that sometimes it is better to postpone calculations till the end.

The total sale on first six days is 5028 + 3042 + 4446 + 786 + 5376 + 2838 = 21516. The average for 6 days is: 21516/6, which gives Rs. 3586.