Practise ‘Average’ problems for faster solutions

Hyderabad: 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 model questions and practice bits along with solutions on the Average topic.

1) There are 10 balls of which some balls are red and the others white. The average cost of all balls is Rs 28. If the average cost of red balls is Rs 25 and that of white balls is Rs 30, the number of white balls is
1) 3                2) 5               3) 6               4) 7
Answer: 3

Solution: W + R = 10 balls
30                    25
28
3                     2

5 parts 10
3 parts ?
3 × 2 = 6.

2) The average age of boys of a school is 12 years and of girls is 11 years. If the total number of boys is 480, then find the number of girls. If the average age of school is 11 years 9 months.
1) 140                      2) 150                      3) 160                     4) 170
Answer: 3

Solution: B              G

12             11

3: 1
3 parts   480
1 part  160
NOTE: Don’t do lengthy calculations
12 – 11 3/4 = 11 + 1 – 11 – 3/4= 1 – 3/4 = 1/4
11 3/4 – 11 = 11 +3/4 – 1 = 3/4

3) A man bought 13 articles at Rs 70 each, 15 articles at Rs 60 each, 12 articles Rs 65 each, then price per article is?
1)  Rs 60.25            2) Rs 64.75             3) Rs 65.75            4) Rs 62.25
Answer: 2
Solution:      13                   15                 12

|                     |                     |

70                  60                 65

Shortcut: Let average = Rs 66
Let average = Rs 66
13 15 12
13 × + 4 15 × -6 12 × – 1
152 -90 -12
-50/40
66 – 50/40
66 – 1.25 = 64.75.

4) The average weight of a class of 65 students is 59 kg. If the average of weight of boys is 63 kg and that of girls is 50 kg, find the number of boys in the class?
1) 45             2) 50             3) 25             4) 20
Answer: 1

Solution: Boys = x,
Girls = 65 – x
x((63)+(65-X)50/65=59
63x + 3250 – 50x = 59 × 65
13x = 3835 – 3250
x = 585/13
x = 45

Shortcut:      B                     G

63                   50

59

9                     4

13 parts  65

1 part  5

9 parts = 9 × 5 = 45

5) If the average score of 42 boys of a school is 137, while the average score of 98 girls is 124 of the same class. Find the combined average of the class.

1) 125.9                   2) 127.9                   3) 130                      4) 132
Answer: 2

Solution: Combined Average
= 42×137 + 98×124
42+98
= 5754 + 12152
140
= 17906
140
= 127.9

Shortcut 1: 137                  124

x

x-124                   137-x

B: G
42 : 98
3 : 7
10 —> 13
X-124
137-x
= 3/7
=> 7x – 868 = 411 – 3x
10x = 1279
x = 127.9

Shortcut 2:  42: 98
3:  7
Let average  = 130 (say)
137                124
+7 × 3           -6 × 7
21                   -42        = -21
130 –  = 131 – 2.1 = 127.9

6. Out of three numbers, the first number is twice of the second and is half of the third. If the average of three numbers is 56, then the difference of first and third numbers is?

1) 12             2) 24             3) 48             4) 20

Answer: 3

Solution:
LCM = 2
a: b : c = 2 : 1 : 4
7 parts  56 × 3
1 part  24
(4 – 2) part  ?
2 × 24 = 48

To be continued..