The following arithmetic reasoning questions are calculation based, database based, ages and venndiagram based.
You have to solve these questions and choose the correct answer from given options.
1. 
In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group,
none can speak any other language. If 2 persons in the group can speak two languages and one person can speak
all the three languages, then how many persons are there in the group?


A.

23


B.

21


C.

24 

D.

22






View Answer
Suppose circles X, Y and Z represent persons who can speak Tamil, Hindi and Gujarati respectively.
Tamilspeaking persons = A + B + D + E = 6 (i)
Hindispeaking persons = B + C + E + F = 15 (ii)
Gujaratispeaking persons = D + E + F + G = 6 (iii)
Persons speaking two languages = B + D + F = 2 (iv)
Persons speaking all 3 languages = E = 1 (v)
Now, putting the value of eq^{n} (v) in (i), (ii), (iii),(iv) subsequently, we get
A + B + D = 5 (vi)
B + C + F = 14 (vii)
D + F + G = 5 (viii)
B + D + F = 2 (ix)
Subtracting (ix) from (vi), we get: A − F= 3 (x)
Adding (vii) and (viii), we get : B + C + D + 2F + G = 19 (xi)
Adding (x) and (xi), we get:
A + B + C + D + F + G = 22
or A + B + C + D + E + F + G = 23
Therefore, Total persons = 23
Hence, option (A) is the correct answer.

2. 
Five hundred candidates appeared in an examination comprising of test in English, Hindi and Maths. The following
diagram show the number of candidates who failed in different tests. What is the percentage of candidates who failed in at
least two subjects?


A.

7.2%


B.

78%


C.

6.8% 

D.

7.8%






View Answer
We can see, the number of candidates who failed in at least two subjects
= number of candidates who failed in two or more subjects.
= (10 + 12 + 12 + 5) = 39
Therefore, the percentage = (39/500 × 100) = 7.8%
Hence, option (D) is the correct answer.

3. 
Reema is twice as old as Seema. Three years ago, shw was three times as old as Seema. How old is Reema now?


A.

14 years


B.

12 years


C.

10 years 

D.

8 years






View Answer
Let Seema's present age is x years.
Then, Reema's present age = 2x years.
Three years ago, Seema's age was (x − 3) and Reema's age was =(2x − 3)
So, as per equation:
(2x − 3) = 3(x − 3)
2x − 3 = 3x − 9
x = 6
Putting the value of x in Reema's present age 2x
= 2 × 6
= 12 years.
Hence, option (B) is the correct answer.

4. 
A, B, C and D play a game of cards. A says to B, "If I give you 8 cards, you will have as many as C has and I shall
have 3 less than what C has. Also, if I take 6 cards from C, I shall have twice as many as D has." If B and D together
have 50 cards, how many cards has A got?


A.

30 cards


B.

45 cards


C.

40 cards 

D.

35 cards






View Answer
We can see:
B + 8 = C (i)
A − 8 = C − 3 (ii)
A + 6 = 2D (iii)
B + D = 50 (iv)
Solving equation (ii)
A − 8 = C − 3 (ii)
A − 8 + 3 = C
or C = A − 5
Putting the value of C, in equation (i), we get:
B + 8 = A − 5
or A − B = 13
or A = 13 + B (v)
From equation (iv) we get the value of D as:
D = 50 − B
putting the value of D, in equation (iii), we get:
A + 6 = 2D
A + 6 = 2(50 − B)
A + 6 = 100 − 2B
A + 2B = 94 (vi)
Now, putting the value of A from equation (v) into equation (iv), we get:
13 + B + 2B = 94
13 + 3B = 94
3B = 94 13
3B = 81
B = 81/3 = 27
Putting the value of B, in equation (v), we get:
A = 13 + 27 = 40
Hence, option (C) is the correct answer.

5. 
A shephard had 16 sheeps. All but nine died. How many was he left with? 

A.

7


B.

9


C.

Nil 

D.

8






View Answer
All but nine died means 'All except nine died' i.e 'nine sheep reamined alive'. Hence, option (B) is the correct answer.

6. 
A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 sholdiers there
is one captain. The number of captains in the group is


A.

75


B.

80


C.

70 

D.

85






View Answer
We see clearly, that out of every 16 persons, there is one captain
So, the number of captains = 1200/16 = 75. Hence, option (A) is the correct answer.

7. 
Amit cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces
is twenty grams in weight. If he has seven pieces of the cake in all with her, what was the weight of original cake?


A.

220 gm


B.

250 gm


C.

200 gm 

D.

240 gm






View Answer
Clearly, the seven pieces consist of 6 smaller equual pieces and one half cake piece
Weight of each small piece = 20 gm (given)
Then, total weight of the cake = 2 × (20 × 6) = 240 gm. Hence, option (D) is the correct answer.

8. 
At the end of a meeting the ten people present all shake hands with each other once.
How many handshakes will there be altogether?


A.

40


B.

45


C.

50 

D.

20






View Answer
We see, that total handshakes = (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) = 45.
Hence, option (B) is the correct answer.

9. 
The number of boys in a class is three times the number of girls. Which one of the following numbers cannot
represent the total number of children in the class?


A.

42


B.

36


C.

48 

D.

52






View Answer
Let the number of girls in the class = x
Then, the number of boys = 3x
Total number of students in the class = x + 3x = 4x
Therefore, to find the exact vlue of x, the total number of students must be divisible by 4.
The options which are divisible by 4 could be the answer while the option which is not divisilbe by 4 can't be
the answer. Hence, option (A) is the correct answer.

10. 
In a caravan in addition to 50 hens, there are 45 goats and 8 camels with some keepers. If the total number
of feet by 224 more than the number of heads in the caravan, the number of keepers is


A.

25


B.

20


C.

15 

D.

12






View Answer
Let the number of keepers = x
The, total number of feet = 2 × 50 + 4 × 45 + 4 × 8 + 2x = 2x + 312
Total numbers of heads = 50 + 45 + 8 + x = 103 + x
Now, as per equation, (2x + 312) = (103 + x) + 224
2x  x = 103 + 224 − 312
x = 15
. Hence, option (C) is the correct answer.
