Arithmetic Reasoning (SSC REASONING) Part-2

Total Questions: 50

31. The average marks of eight students in the Mathematics exam are 75. If the highest and lowest marks are removed, then the average marks become 80. If the ratio of the highest marks to the lowest marks is 3: 1, then the highest marks are what percentage of the sum of the marks obtained by the eight students in the Mathematics exam?

Correct Answer: (a) 15%
Solution:Total marks = 75 x 8 = 600
Total marks (except highest and lowest
marks) = 6 x 80 = 480
Highest + lowest = 3:1 = 120
Highest = 90
Percentage of marks scored by the
topper = 90/600 × 100 = 15%

32. In a class of 68 students, 34 students participated only in Debate and 8 students participated in both Quiz and Debate. If every student of the class has participated in at least one of these two competitions, how many students participated in Quiz?

Correct Answer: (b) 34
Solution:Students who participated in debate = 34
Students who participated in both debate
and quiz = 8
Students who participated only in debate
= 34-8 = 26
Total number of students who
participated in Quiz = 68 - 26 -8 = 34

33. One day, 90 students were travelling in a bus and the ratio of the number of boys to that of girls was 2: 1, The next day, the number of students remained the same, but the ratio of the number of boys to that of girls became 3 : 2. What was the difference between the number of boys travelling in the bus on both the days?

Correct Answer: (a) 6
Solution:Total number of students = 90
Day 1 ratio of boys and girls = 2:1
so the number of boys and girls= 60 and
30 respectively.
Next day ratio of boys and girls = 3:2
So number of boys =3/5
So the difference between boys on both
days = 60 -54 = 6x 90 = 54

34. Two numbers are named as Number A and Number B. The sum of Number A, Its square and its cube is 399. The sum of Number B, its square and its cube is 819. What would be the square of the number obtained by adding Number A and Number B?

Correct Answer: (d) 256
Solution:a + a²+ a³ = 399
b+ b²+b³ = 819
Using hit and trial we can say that
a = 7 and b = 9 as 8³ > 399
So (a + b)² = 16² = 256.

35. A total of 60 students are traveling in a bus. The ratio of the number of boys to that of girls is 2: 1. Then, 15 boys get down and 5 girls get in the bus at the first stop, and 5 boys get in and 10 girls get down from the bus at the second stop. What is the ratio of the number of boys to that of girls on the bus after the second stop?

Correct Answer: (c) 2:1
Solution:nitially boys = 40 and girls = 20
After first stop, Boys = 40- 15 = 25
and girls = 20 + 5 = 25
After second stop, Boys = 25 + 5 = 30
and girls = 25- 10 = 15
Required ratio is = 30: 15 = 2:1

36. The sum of a number's square, its cube and its next number's cube is 205. What is the number?

Correct Answer: (c) 4
Solution:a²+ a³+ (a + 1)³ = 205
a = 4 satisfies the equation

37. When a number is added to its next number and another number that is four times its next number, the sum of these three numbers is 95. Find the number.

Correct Answer: (a) 15
Solution:According to the question
X+X+1+ 4 (X+ 1) = 95
= 6X + 5 = 95, So 6X = 90 and X = 15

38. In a group of 73 friends, 14 friends go to Gym and Karate classes both, whereas 7 friends neither go to Gym class nor to Karate class. If a total of 36 friends go to Gym class, then how many friends go to only Karate class?

Correct Answer: (a) 30
Solution:Friends who either go to Gym
or Karate = 73 -7 = 66
Friends who go only Karate class
= 66 - 36 = 30

39. ₹2,871 is to be divided among A, B and C in the ratio of 9:11:13, respectively. How much more money (in) will C get as compared to A?

Correct Answer: (b) ₹ 348
Solution:)a+b+c = 2871
Let a = 9R, b = 11R, c = 13R
33R = 2871⇒ R = 2871/33 = 87
Difference of ratio between A & C
is 4R, So 4 x 87 = 348

40. Identify the number which when added to itself 14 times gives 195.

Correct Answer: (d) 13
Solution:x + 14x = 195
15x = 195x = 13