Interlinking the Concept of Alligations and Weighted Averages Video Lecture

In this video I have started with the topic of averages and then weighted averages. The most important thing that I have explained in this video is that I have interlinked the concept of weighted averages and alligation and have shown that there is basically no difference between both of them and they are the manifestation of the same concept in two different manners.

Average = Sum of all quantities/Total number of quantities

Example discussed of a class of 5 students having weight/age as 42,55,58,65,50

Average is termed as the mean of all values provided to use.

One more method explained by me of calculating averages where we will suppose any arbitrary number N and then average would be the sum of N and the summation of differences between the individual numbers and N divided by the number of numbers.

Some properties of Averages - 

1. The average will always lie between the smallest and the largest numbers.

2. If we add, substract, multiply and divide all the numbers by a common constant k, the value of average will be increased, decreased, multiplied and divided respectively by the same constant.

Questions discussed by me in this video -

Question 1. Three years ago, the average of X,Y and Z was 27 years and that of Y and Z, 5 years ago was 20 years. X's present age would be ?

Question 2. Rohan Gavaskar has a certain average for 9 innings. In the tenth inning, he scored 100 runs thereby increasing his average by 8 runs. His new average is ?

Question 3. The average of 71 results is 48. If the average of first 59 results is 46 and that of last 11 is 52. Find the 60th result ?

Question 4. 19 persons went to a bakery shop for eating cakes. 13 of them spent Rs. 79 each for eating cakes and the remaining 6 spent Rs. 4 more than the average expenditure of all the 19. What is the total money spent by them ?

Question 5. 4 kg of rice at Rs. 5 per kg is mixed with 8 kg rice at Rs. 6 per kg. Find the average price of the mixture ?

Question 6. The average salary of the entire staff in an office is Rs. 3200 per month. The average salary of officers is Rs. 6800 and that of non officers is Rs. 2000. If the number of officers is 5, then find the number of non officers in the office ?

Question 7. The average of students in class A is 16.75 years. 20 new students with an average age of 13.25 years join the group because of which the average of the new class lowers down to 15 years. Find the number of students which were initially present in the class ?

Question 8. Two varieties of pulses are mixed in the ratio 2:3 . The cost price of each kg of the first variety of pulse is Rs. 5 more than the cost price of each kg of second variety of pulse. The mixture is sold at 20 % profit at Rs. 30 per kg. Find the cost price of first and second variety of pulses ?

Question 9. A retailer has two varieties of apples A1 and A2 costing Rs. 10 per kg and Rs. 12 per kg respectively. He sells the combination of those apples having 420 kg of A1 apples for Rs. 25200 at a profit of 20 %. How many kilograms of A2 apples were present in the combination ?

Question 10. How many oranges at 5 for Rs. 23 should be mixed with 200 oranges at 7 for Rs. 42 so as to sell them at Rs. 72 per dozen with a 20 % gain ?

Question 11. The average of the marks obtained by 54 students in a class is 82. Find the marks of the top scorer, if the average of the others is 1 less than the average marks of all the students in the class ?