Suppose circles X, Y and Z represent persons who can speak Tamil, Hindi and Gujarati respectively. Tamil-speaking persons = A + B + D + E = 6 -------------(i)
Hindi-speaking persons = B + C + E + F = 15 -------------(ii)
Gujarati-speaking 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 eqⁿ (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.

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.

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.

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.

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

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.

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

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.