Average of 14th innings = x
Average of 15th innings = x+2
∴ 14x+72 = 15(x+2)

Correct Option: A

Let the average of 14th innings = x
∴ Average of 15th innings = x+2
Then, 14x+72 = 15(x+2)
⇒ 14x+72 = 15x +30
∴ x = 42
∴ Average for 15th innings = x+2 = 42 + 2 = 44

New average = (sum of 5 observation + sum of 3 new numbers) / 8

Correct Option: B

Total of 5 observations = 5 x 15 = 75

New sum = 75 + 16.5 + 18 + 14.5 = 124

New Average = 124 ⁄ 8 = 15.5

x₁ + x₂ + x₃ = 3 x 14 = 42 ....(i)
and (x₁ + x₂) x 2 = 30 ...(ii)
solve both equation and find x₁

Correct Option: B

x₁ + x₂ + x₃ = 3 x 14 = 42 ....(i)
and (x₁ + x₂) x 2 = 30
⇒ x₁ + x₂ =15 ....(ii)
From Eqs. (i) and (ii), we get
x₁ + 15 = 42
∴ x₁ = 42 - 15 = 27

Sum of the age of all students = sum of the age of 45 students + sum of the age of 15 students

Average age of all student = sum of age of all students / 60

Correct Option: B

Sum of the age of 45 students = 45 x 13 = 585 yr

Sum of the age of 15 students = 15 x18 = 270 yr

Sum of the age of all students = sum of the age of 45 students + sum of the age of 15 students
= 585 yr + 270 yr
=855 yr

∴ Average age of all students = 855 ⁄ 60
= 14.25 yr

Let the number of non-officers be y.

Sum of salary of the entire = 120y + 550 x 16

The average salary of the entire staff = Sum of salary of the entire staff / ( 16+y )

Correct Option: C

Let the number of non-officers be y.

Then number of entire staff = 16 + y

Sum of total salary = 200(16 + y)
=16 x 550 + 120y
⇒ 120y + 550 x 16 = 200x16 + 200y
⇒ 3y +220 = 80 + 5y
⇒ 2y = 140
∴ y = 140/2 = 70