## Average

#### Average

1. A batsman has a certain average of runs for 14th innings. He scores 72 runs in the 15th innings, thus his average increased by 2. Find the average after 15th innings.
1. 44
2. 46
3. 42
4. 48

1. 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

1. The Average of 5 observation is 15. If three new observation 16.5, 18 and 14.5 be added. Then find the new average.
1. 14.8
2. 15.5
3. 16.2
4. 15.6

1. 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

1. The average of x1, x2 and x3 is 14. Twice the sum of x2 and x3 is 30. What is the value of x1 ?
1. 20
2. 27
3. 16
4. 2

1. 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

1. The average age of 45 students in a class in 13 yr, 15 new students with an average age of 18 yr join the class. What is the average age of all the students in the class?
1. 13.15 yr
2. 14.25 yr
3. 12.28 yr
4. 16.42 yr

1. 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

1. The average salary of the entire staff in an office is ₹ 200 per day. The average salary of officers is ₹ 550 and that of non officers is ₹ 120. If the number of officers is 16, then find the number of non officers in the office.
1. 72
2. 60
3. 70
4. 65

1. 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