Formulae and shortcuts used to solve the following problems are discussed in the previous post.
Solved Examples
1. What is the average of 10, 20, 30, 40, 50?
Soln:
Method 1:
No. of values: 5
Avg = (10+20+30+40+50)/5 = 30
Method 2:
As the given values are in A.P., we can use shortcut as follows:
Avg = (10+50)/2 = 30
2. If the Arithmetic mean of 10 terms is 20, find the sum of the terms?
Soln: Sum = avg * no. of units = 20 * 10 = 200
3. If the average marks of 2 students is 80 and the 3rd student with 68 marks joined, then find the average of 3 students?
Soln:
Total marks of 2 students = 80*2=160
Total marks of 3 students = 160+68 = 228
Avg of 3 students = 228/3 = 73 marks
4. If the average marks of 2 students is 80 and when the 3rd student joined, the average increased to 82. Find the marks of 3rd student?
Soln:
Method1:
Total marks of 2 students = 80*2=160
Total marks of 3 students = 82*3 = 246
Marks of 3rd student = 246-160=86marks
Method2 (by glance):
As the 3rd student joined, the avg increased by 2 marks for 3 students => total 3*2 = 6marks
So the marks of 3rd student = 80+6=86 marks
5. If the average of marks of first 10 students of a class is 50, and the average of next 20 students is 75, find the average marks of the class if the total strength is 30?
Soln:
Here there are 2 sections of people. So we need to take weighted average.
Avg = (mp + nq)/(m + n)
ð Avg = (10*50 + 20*75)/(10+20) = (500+1500)/30 = 2000/30
6. If the average of marks of first 10 students of a class is 50, and the average of next 20 students is 75, find the average marks of the class if the total strength is 40?
Soln:
The details are given for first 10+20 = 30 students, but the class strength is 40.
So the class average cannot be determined as we don’t know the details of last 10 students.
7. If the 2 persons average age is 25, find the avg age after 5 years?
Soln:
After 5 years, age of both persons will increase by 5 years.
So avg age will be increased by 5 years = 25 + 5 = 30 years
8. If the 2 persons average age is 25, find the avg age before 5 years?
Soln:
Cannot be determined for the following reason:
Let present age of 2 persons be 46 and 4 years.
Before 5 years, 1st person age = 46 – 5 = 41 years
2nd person age = 4-5 = -1 which is not possible, i.e. 2nd person is not yet born before 5 years. So, in this particular scenario, the avg age before 5 years cannot be determined.
9. Find the average of 79, 87, 93, 82?
Soln:
Method1:
Avg =( 79+87+93+82)/4 = 341/4 = 85.25
Method2:
As the above given numbers are large no.s, instead of adding directly, we can follow as below:
Assume the avg as 80, and add or subtract each no. accordingly as follows:
New sub avg = (-1+7+13+2)/4 = 21/4 = 5.25
Therefore, avg = 80+5.25 = 85.25
Same is the shortcut for weighted averages.
10. If the average of first half of class is 20marks and the average of remaining half of the class is 24, find the average of the class?
Note: As the no. of students is same in first and next half of the class, avg of the class cab be determined as the mean of two averages.
11. If the average of boys is 20 marks and the average of girls is 24, find the combined average of boys and girls?
Soln:
Cannot be determined as the no. of boys and girls is unknown.
12. If the ratio of averages of 10 boys and 20 girls is 3:2, find the combined average?
Soln:
Cannot be determined because of the following reason:
Let average of 10 boys be 3x
Average of 20 girls be 2x
Combined average = (3x + 2x)/30 -> cannot be determined as x is unknown.
Note: If the ratio of averages is given, then the combined average cannot be determined.
Answer 3 - 228/3 = 76 not 73
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