Find the average of these problems

This article is in continuation to the last article on arithmetic that will aid you in your preparation for government recruitment exams. Here are some examples along with solutions on the Average topic.

1. Find the average of the first 15 whole numbers

a) 7 b) 8 c) 9 d) 10

Solution: 0,1,2,…..14
Here the gap is the same
(0 + 14 )/2 = 14/2 = 7

Note: If ‘0’ is one of the quantities of a given data, then that ‘0’ will also be included while calculating the average.

2. Find the average of 36, 28, 45, 63, 50

a) 40.4 b) 42.4 c) 44.4 d) 46.4

Solution: Here the gap is not the same
Thus, the method for average
= sum of no.s/ total no.s
= 36 + 28 + 45 + 63 + 50/5 = 222/5 = 44.4

Shortcut method: Assume that average = 50
36 – 50 = 14
28 – 50 = -22
45 – 50 = -5
63 – 50 = 13
50 – 50 = 0
-14 – 22 – 5 + 13 + 0
= -28
50 – 28/5 = 50 – 5.6 = 44.4

3. What is the average of all the multiples of 6 from 20 to 80?

a) 48 b) 50 c) 51 d) 52

Solution: 24, 30, …..78
Here, the gap is the same
24 + 78/2 = 102/2 = 51

4. a, b, c, d, e, f, g are consecutive even numbers. j, k, l, m, n are consecutive odd numbers. Then, the average of all the numbers is

a)(a + b + m + n)/4 b)(f + c + n + g)/4
c) 3(a + n/2) d) l + d/n

Solution: a, b, c, d, e, f, g; average = d
j, k, l, m, n; average = l
Average of all numbers = (d + l)/2

Note: Here the gap is same. So the average is the middle number.

5. The average of five consecutive odd numbers is 27. What is the product of the first and the last number?

a) 621 b) 667
c) 713 d)725

Solution: Since the gap between the consecutive odd numbers is same, the average will be the middle number. Thus, the numbers are:
23, 25, 27, 29, 31
Product of 23 × 31= 713

To be continued…

 

M Venkat
Director
MVK Publications
Dilsukhnagar
7671002120