## Average

#### Average

1. Out of the three annual examinations, each with a total of 500 marks, a student secured average marks of 45% and 55% in the first and second annual examinations. To have an overall average of 60%, how many marks does the student need to secure in the third annual examination ?
1. 450
2. 400
3. 350
4. 300

1. Total marks for three examinations = 3x 500 = 1500
Marks secured in first examination = 45 % of 500
Marks secured in second examination = 55 % of 500
Marks required in third test = 60% of total marks for three examination - sum of marks secured in first two examinations

##### Correct Option: B

Total marks for three examinations = 3x 500 = 1500

Total required marks in three examinations = 60% of 1500
=( 3 x 500 x 60 ) / 100
= 900

Marks secured in first examination = 45 % of 500
=( 500 x 45 ) / 100
=225

Marks secured in third examination = 55 % of 500
=( 500 x 55 ) / 100
=275

Thus, the required marks in third examination
=900 - ( 225 + 275 )
=900 - 500
= 400

1. The average age of women and child workers in a factory was 15 yr. The average age of all the 16 children was 8 yr and average age of women workers was 22 yr. If 10 women workers were married, then the number of unmarried women workers was.
1. 16
2. 12
3. 8
4. 6

1. Let the number of women workers be Y.

Then, 22y + 16 x 8 = 15 (16+y)

##### Correct Option: D

Let the number of women workers be Y.

Then, 22y + 16 x 8 = 15 (16+y)
⇒ 22y + 128 = 240 + 15y
⇒ 22y - 15y= 240 - 128
∴ y = 16

∴ Unmarried women workers = 16 - 10 = 6

1. If the average age of Dinesh and Mahesh is 16 yr, the average age of Mahesh and Rahul is 13 yr and the average age of Dinesh and Rahul is 14 yr, then what is the age of Mahesh?
1. 15 yr
2. 20 yr
3. 58 yr
4. 16 yr

1. Let ages of Dinesh, Mahesh and Rahul be D, M and R, respectively.
Then,
D + M = 2 x 16 = 32
M + R = 2 x 13 = 26
D + R = 2 x14 = 28

##### Correct Option: A

Let ages of Dinesh, Mahesh and Rahul be D, M and R, respectively.
Then,
D + M = 2 x 16 = 32 ...(i)
M + R = 2 x 13 = 26 ....(ii)
D + R = 2 x14 = 28 ....(iii)

On adding Eqs. (i), (ii) and (iii), we get
2(D + M + R) =86
⇒ D + M + R = 43 ....(iv)

On subtracting Eqs. (iii) from Eq. (iv), we get
M = 43 - 28
∴ M = 15 Yr

1. In a class, there are 80 students and their average marks in the annual examination are 40. If the average marks of passed students are 60 and average marks of failed students are 35, then find out the number of students who failed.
1. 63
2. 60
3. 72
4. 64

1. Let the number of failed student = Y
so 80 x 40 = (80 - Y) x 60 + 35Y

##### Correct Option: D

Let the number of failed student = Y
∴ Number of passed student = 80 - Y

sum of marks of all students = sum of marks of passed students + sum of marks of failed students
80 x 40 = (80 - Y) x 60 + 35Y
⇒ 3200 =4800 - 60Y + 35Y
⇒ 25Y = 1600
∴ Y = 64
∴ Number of students who failed = 64

1. Last year Sahara, Tata, Singhania and Birla each has 250 industries. This year everyone has sold out 10 factories due to the recession of the economy and poor turnout. The average number of industries which of them now has
1. 260
2. 240
3. 25
4. none of these

1. Required average
= Old average - Sold average

##### Correct Option: B

Required average
= Old average - Sold average
= ( 250 ) - ( 10 ) = 240