# Problems on Average for NIACL Assistants

Problems On Average Practice Test
1.The average weight of a group of 53 girls was calculated as 58 kg. It was later discovered that the weight of one of the girls was read as 65 kg., whereas her actual weight was 45 kg. What is the actual average weight of the group of 53 girls ? (rounded off to two digits after decimal)
a)58.62 kg.
b)58.37 kg.
c)57.37 kg.
d)57.62 kg.
e)None of these

2.The average marks in Science subject of a class of 20 students is 68. If the marks of two students were misread as 48 and 65 of the actual marks 72 and 61 respectively, then what would be the correct average ?
a)68.5
b)69
c)69.5
d)70
e)66

3.The average weight of 45 students in a class was calculated as 36 kg. It was later found that the weight of two students in the class was wrongly calculated. The actual weight of one of the boys in the class was 32 kg., but it was calculated as 34 kg. and the weight of another boy in the class was 45 kg., whereas it was calculated as 40 kg. What is the actual average weight of the 45 students in the class ? (rounded off to two digits after decimal)
a)36.07 kg.
b)36.16 kg.
c)35.84 kg.
d)Can't be determined
e)None of these

4.Average score of Rahul, Manish and Suresh is 63. Rahul's score is 15 less than Ajay and 10 more than Manish. If Ajay scored 30 marks more than the average score of Rahul, Manish and Suresh, what is the sum of Manish's and Suresh's scores?
a)120
b)111
c)117
d)Can't be determined
e)None of these

5.The average speed of a car is 5/7th of that of a bus. The bus covers 750 km. in 10 hours. How much distance (in km) will the car cover in 7 hours ?
a)375
b)285
c)365
d)295
e)None of these

6.Of the three numbers, the average of the first and the second is greater than the average of the second and the third by 15. What is the difference between the first and the third of the three numbers ?
a)15
b)45
c)60
e)None of these

7.A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was:
a)645
b)665
c)588
d)672
e)None of these

8.The sum of five numbers is 555. The average of first two numbers is 75 and the third number is 115. What is the average of last two numbers ?
a)145
b)150
c)265
d)290
e)None of these

9.The average of 8 numbers is A and the average of four of these is B. If the average of remaining four is C, then
a)2A = B + C
b)A = B + 2C
c)A = 2B + C
d)A = 2A + 2B
e)None of these

10.The average score of a class of boys and girls in an examination is A. The ratio of boys and girls in the class is 3:1. If the average score of the boys is (A + 1), the average score of the girls is :
a)(A - 1)
b)(A - 3)
c)(A + 1)
d)(A + 3)
e)None of these

1.d)
2.b)
3.a)
4.b)
5.a)
6.e)
7.b)
8.a)
9.a)
10.b)

Solution
1.Decrease in weight = (65 -45) = 20 kg.
Required actual average weight = (58 - 20/53) = 57.62 kg.

2.Difference of marks = 72 + 61 - 48 - 65 = 20
Therefore, correct average marks
= 68 + (20/20)
= 69

3.Actual weight of all the students
= 36 × 45 - 34 + 32 - 40 + 45
= 1623 kg.
Therefore, actual average weight = (1623/45) = 36.07 kg.

4.Ajay's score = 63 + 30 = 93
Rahul's score = 93 - 15 = 78
Sum of Manish's and Suresh's scores
= 3 × 63 - 78 = 111

5.Average speed of bus = (750/10) = 75 kmph.
Speed of car = 5/7 × 75 = 375/7 kmph.
Distance covered by car in 7 hours
= 375/7 × 7 = 375 km.

6.Let the three numbers be x, y and z.
then, [(x + y)/2] - [(y + z)/2] = 15
or, (x + y - y - z)/2 = 15
or, x - z = 30

7.The number of points team scored
= 8 × 84 - 92 + 85
= 665

8.Sum of last two numbers
= 555 - (2 × 75) - 115
= 290
Required average = (290/2) = 145

9.8A = 4B + 4C
or, 2A = B + C

10.Average marks of girls = x (let)
now, A = [3 × (A + 1) + x]/(3 + 1)
or, 4A = 3A + 3 + x
or, x = A - 3 