Let a, b, c are the ages of A, B and C respectively

a + b = 2 X 20 = 40 ...(1)
b + c = 2 x 19 = 38 ...(2)
c + a = 2 x 21 = 42 ...(3)

Adding all the 3 equalities
2a + 2b + 2c = 120
a + b + c = 60 --- (4)

From eq. (2) and (4)
a = 22
From eq. (1) and (4)
b = 18
From eq. (4)
c= 20

Correct Option: C

Let a, b, c are the ages of A, B and C respectively

a + b = 2 X 20 = 40 ...(1)
b + c = 2 x 19 = 38 ...(2)
c + a = 2 x 21 = 42 ...(3)

Adding all the 3 equalities
2a + 2b + 2c = 120
a + b + c = 60 --- (4)

From eq. (2) and (4)
a = 22
From eq. (1) and (4)
b = 18
From eq. (4)
c= 20

∴ Age of A = 22 years
Age of B = 18 years
Age of C = 20 years

Average of consecutive even numbers = (First number + Last number)/2

Correct Option: D

Even numbers between 11 to 63
= 12,14,16,18,20,..........,62.
Clearly, this is a series of consecutive even number

According to the formula
Average of consecutive even numbers = (First number + Last number)/2
= (12 + 62)/2
= 74/2
= 37

Average of the cubes os 1st 'n' natural numbers= n(n+1)²/4

Correct Option: C

As per the formula,
Average of the cubes os 1st 'n' natural numbers= n(n+1)²/4
where, n= 5.

∴ Required average = 5(5+1)²/4
= (5 x 36)/4 = 5 x 9= 45

Average of 8 numbers = 14
Sum of 8 numbers = 14 x 8 = 112
Similarly, average of 6 numbers = 16
Sum of 6 number = 16 x 6 = 96
∴ Sum of remaining two number
= Sum of 8 number - sum of 6 numbers

Correct Option: C

Average of 8 numbers = 14
Sum of 8 numbers = 14 x 8 = 112
Similarly, average of 6 numbers = 16
Sum of 6 number = 16 x 6 = 96
∴ Sum of remaining two number
= Sum of 8 number - sum of 6 numbers
= 112- 96 = 16
Average = (sum of two number)/2 = 16/2 = 8

Age of 5th boy = (sum of age of 5 boys) - (sum of age of 4 boys)

Correct Option: A

Average of 5 boys = 16 yr
sum of age of 5 boys = 16 x 5 = 80 yr
∴ Average age of 4 boys = 16 - yr 3 month
= 16 yr + 3/12 yr = 16 yr + 1/4 yr
Sum of ages of 4 boys = 4 x (16 +1/4) yr
= 64 +1 = 65 yr
∴ Age of 5th boy = (80 - 65) yr = 15 yr