Sample questions to ace SI examinations

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exams. Here are some subject-wise previously asked questions and answers along with explanations. AVERAGE Average is a simple topic and just involves simple mathematical calculations. This concept has various applications. Firstly, we will understand the basics of […]

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exams. Here are some subject-wise previously asked questions and answers along with explanations.

AVERAGE

Average is a simple topic and just involves simple mathematical calculations. This concept has various applications. Firstly, we will understand the basics of the topic. Average is just a mean value of all the given observations or we can say it is an arithmetic mean of observations.

Average =(Sum of all observations)/(Number of observations )
Example1: Find an average of following observations:
53, 54, 58, 62, 52, 55, 51
Solution: Average = (Sum of all observations)/(Number of observations )
Average = (53 54 58 62 52 55 51 )/7
So, Average = 55

Properties of Average:
i) Average lies between maximum and minimum observation.

ii) If value of each observation is multiplied by some value ‘N’, then
Average will also be multiplied by the same value i.e. N.
For example: Assume the previous set of observations. If 2 is multiplied with all observations, then new observations will be as follows:

6, 8, 16, 24, 4, 10, 2

New Average = 707 = 10 = 2(5) = 2 × Old Average

iii) If value of each observation is increased or decreased by some number, then average will also be increased or decreased by the same number.
For example: Continuing with the same example. If 2 is added to all observations, then new observations will be as follows:
5, 6, 10, 14, 4, 7, 3
New Average = 49/7 = 7 = 5 2 = 2 Old Average
iv) Similarly, if each observation is divided by some number, then average will also be divided by same number.

For example 1: If 2 is divided from all observations, then new observations will be as follows:

1.5, 2, 4, 6, 1, 2.5, 0.5

New Average = 17.57 = 2.5 = 52

Therefore, we can say any general operation applied on observations will have same effect on average.

Formulae:
If the number of quantities in two groups be ‘m’ and ’n’, and their averages are x and y respectively. Then the average of all of them put together = mx ny /m n

If the average of m quantities is x and the average of n quantities out of them is y, then the average of remaining group = mx – ny/ m-n

The average of n quantities is equal to x. When a quantity is removed, the average becomes y. The value of the removed quantity is n(x – y) y
The average of n quantities is equal to y. When a quantity is added, the average becomes y. The value of the new quantity is n(y – x) y.
Questions

1 The average of 40 numbers is 35. If two numbers 44, 45 are discarded, then the average of the remaining numbers is (SI mains 2018)

a) 33.5 b) 34 c) 34.25 d) 34.5

Ans: d

According to the question

Average of 40 numbers is = 35

Sum of 40 numbers is = 40 × 35 = 1400

Two numbers discarded = 44 45 = 89

Sum of 38 numbers = 1400 – 89 = 1311

Average = 1311/38= 34.5

2 There are 4 numbers, the average of first 3 numbers is 56 and the average of last 3 numbers is 49. If the first number is 48, then the last number is (SI mains 2018)

a) 40 b) 55 c) 39 d) 27

Ans: d

Assume that the given four numbers are represented by a, b, c and d.

a b c = 56*3 = 168—- (1)

b c d = 49*3 = 147— (2)

a = 48 substitute first number in the first equation then

b c = 168 – 48 = 120

Substitute this value in the second equation, then
120 d = 147 –>; d = 147 – 120 = 27

3 If the average age of three persons is 20 years and the ages are in the ratio 2:3:5, then the age (in years) of the youngest among them is (SI mains 2018)

(a) 12 (b) 18 (c) 10 (d) 8

Ans: a

Let the ages of three persons according to the question be 2x, 3x and 5x.

According to the question, (2x 3x 5x)/3 = 20
Hence 10x = 60
So x = 6

Hence, the age of the youngest is 2x = 12
To be continued…

Banda Ravipal Reddy
Director, SIGMA

Sai Institute of General Mental Ability