Arithmetic questions from previous SI exam papers

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 4 The following table is the marks of 20 students of a class in mathematics. The average mark of these 20 students is(SI […]

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
4 The following table is the marks of 20 students of a class in mathematics. The average mark of these 20 students is(SI mains 2018)
Marks 80 85 90 95 100
No.of students 2 4 7 4 3
(a) 89.5 (b) 90 (c) 90.5 (d) 91
Ans: c
Sum of marks= 80*2 85*4 90*7 95*4 100*3
=160 340 630 380 300=1810
Required average= 1810/20=90.5
5 There are 60 students in a class and one of the students weighing 40 kg was replaced by another student. Now, the average weight of the students increases by 0.2kg. The weight of the new student in (kg) (SI mains 2018)
(a) 48 (b) 52 (c) 54 (d) 56
Ans: b
The average increases only when the weight of the new person is more than the weight of the old person.
Over all increased weight= 60*0.2=12kgs
New persons weight= 40 12= 52

6 The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older than captain. If the average age of the remaining 9 members is 1 year less than the average age of the whole team then the average age of the whole team is(SI prelims 2018)
a) 22yrs b) 23yrs c) 25yrs d) 24yrs
Ans: b

Let the average age of the whole team by x years.

∴11x−(26 29)=9(x−1)

⇒11x−9x=46

⇒2x=46
⇒x=23.

So, average age of the team is 23 years.
7 The average age of 28 students of a class is 12 years. If their teacher’s age is included the average age increases by one year. Then the age of the teacher in years is(SI 2016)

a) 41 b) 40 c) 39 d) 38

Ans: a

Sum of age of 28 students is=28*12=336

After adding teacher, the new average= 12 1 =13
The sum of age of 29 persons =13*29=377

Teacher’s age = 377 – 336 = 41
8 A batsman in his 12th innings makes a score of 63 runs and there by increased his average score by 2 runs. The average of his score after 12th innings is(SI 2016)

a) 42 b) 41 c) 35 d) 34

Ans: b

Let the total number of runs in 11 innings be “x”.

So, the average number of runs in 11 innings is x/11.
Let the total number of runs in 12 innings after scoring 63 runs in 12th innings be x 63.

Average number of runs in 12th innings is = (x 63)/12

(x 63)/12 = (x/11) 2
=>; (x 63)/12 = (x 22)/11
=>; 11(x 63) = 12(x 22)

=>; 11x 693 = 12x 264

=>; 693 – 264 = 12x – 11x

.°. x = 429
The average of his score after 12th innings
= (x 63)/12= (429 63)/12= 492/12= 41
9 The average of 9 numbers is 30. If the average of first 5 numbers is 25 and that of the last 3 numbers is 35 then the 6th number is(SI 2016)
a) 20 b) 30 c) 40 d) 50
Ans: c
Sum of 9 numbers = 30×9 = 270
Sum of first five numbers = 25×5 = 125

Sum of last three numbers = 35×3 = 105

6th number is = 270 – 125 – 105 = 40
10 In a class having 40 boys and some girls, the average age of the boys and girls are 13.5 years and 13 years respectively. The average age of the whole class is 13years then the number of girls in the class is(SI 2016)

a) 10 b) 11 c) 13 d) 20

Ans: a

There are 40 boys in the class with average age 13.5 years.

Assume that there are x girls in the class with average age 13 years.

If the average age of the whole class is 13.4 years, then we can write the equation((40*13.5) 13x)/(40 x)=13.4

⇒540 13x=536 13.4x

⇒ 0.4x=4

⇒ x= 10.
Therefore, there are 10 girls in the class.
To be continued…

Banda Ravipal Reddy

Director, SIGMA
SaiInstitute of General Mental Ability