# Problems on Average

Q11. The average weight of 8 men is increased by 1.5 Kg when one of the men who weights 65 Kg is replaced by a new man. The weight of the new man is

(a) 65 Kg

(b) 77 Kg

(c) 82 Kg

(d) 90 Kg

**Answer:** (b) 77 Kg

Total increased weight = (1.5 X 8) Kg = 12 Kg

Weight of replacing man = 65 Kg

∴ New man weight = (65 + 12) Kg = 77 Kg

Q12. When the average age of a husband and wife and their son was 42 years. The son got married and a child was born just one year after their marriage. When child turned to be 5 years, then the average age of the family became 3 years. What was the age of daughter-in-law at the time of marriage ?

(a) 25 years

(b) 26 years

(c) 27 years

(d) 28 years

**Answer:** (a) 25 years

Let, the required age of daughter-in-law be x years

At the time of son's marriage

Husband + Wife + Son = 42 X 3 = 126 years

After 6 years of marriage

(42 + 6)3 + 5 + (x + 6) = 36 X 5

⇒ 144 + 5 + x + 6 = 180

⇒ x = 180 - 155 = 25 years

Q13. The average monthly salary of the workers in a workshop is Rs. 8500. If the average monthly salary of 7 technicians is Rs. 10,000 and average monthly salary of the rest is Rs. 7800, the total number of workers in the workshop is

(a) 20

(b) 22

(c) 25

(d) 28

**Answer:** (b) 22

Let, the total no. of workers be x

A/Q | (7 X 10000) + (x - 7) X 7800 | = 8500 |

x |

⇒ 70000 + 7800x - 54600 = 8500x

⇒ 700x = 15400

⇒ x = 22

Q14. The mean of five numbers is 18. If one number is excluded, their mean is 16. The excluded number is

(a) 21

(b) 23

(c) 26

(d) 29

**Answer:** (c) 26

Sum of 5 numbers = 18 X 5 = 90

Sum of 4 numbers = 16 X 4 = 64

∴ The excluded number = 90 - 64 = 26

Q15. The average of a_{1}, a_{2}, a_{3}, a_{4} is 16. Half of the sum of a_{2}, a_{3}, a_{4} is 23. What is the value of a_{1}

(a) 18

(b) 21

(c) 26

(d) 31

**Answer:** (a) 18

a_{1} + a_{2} + a_{3} + a_{4} |
= 16 |

4 |

⇒ a_{1} + a_{2} + a_{3} + a_{4} = 64 ------- (1)

Again | a_{2} + a_{3} + a_{4} |
= 23 |

2 |

⇒ a_{2} + a_{3} + a_{4} = 46 ------ (2)

(1) - (2) ⇒ a_{1} = 64 - 46 = 18

Q16. The average of marks of 28 students in Mathematics was 50. Eight students left the school and then this average is increased by 5. What is the average of marks obtained by the students who left the school ?

(a) 30.5

(b) 32.6

(c) 35

(d) 37.5

**Answer:** (d) 37.5

Sum of marks of 28 students = 28 X 50 = 1400

Average of 20 students = 50 + 5 = 55

Sum of the marks of 20 students = 20 X 55 = 1100

Sum of marks of 8 students = 1400 - 1100 = 300

Average marks of 8 students = 300/8 = 37.5

Q17. A train moves with a speed of 30 km/h for 12 minutes and for next 8 minutes at a speed of 45 km/h. The average speed of the train is

(a) 32 km/h

(b) 36 km/h

(c) 38 km/h

(d) 41 km/h

**Answer:** (b) 36 km/h

At the speed of 30 km/h

Distance covered in 12 minutes = (30/60) X 12 km = 6 km

At the speed of 45 km/h, distance covered in 8 minutes = (45/60) X 8 Km = 6 km

Total Distance covered = 6 km + 6 km = 12 km

Time taken = 20 minutes = 20/60 h = 1/3 h

∴ Average speed = | 12 | km/h |

1/3 |

= 36 Km/h

Q18. w, x, y, z are four consecutive odd numbers. Their average is

(a) w + 2

(b) w + 3

(c) w + 4

(d) w + 6

**Answer:** (b) w + 3

We have

x = w + 2

y = x + 2 = w + 2 + 2 = w + 4

z = y + 2 = w + 4 + 2 = w + 6

Average = | w + x + y + z |

4 |

= | w + w + 2 + w + 4 + w + 6 |

4 |

= | 4w + 12 |

4 |

= w + 3

Q19. The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. The average age of these two women is

(a) 41 years

(b) 45 years

(c) 48 years

(d) 53 years

**Answer:** (c) 48 years

Increased age = 2 X 8 = 16 y

Total age of two men = 35 + 45 = 80 y

Total age of new women = 80 + 16 = 96 y

∴ Average age of women = 96/2 = 48 years

Q20. Of the three numbers, second is twice the first and is also thrice the third. If the average of three numbers is 44, the largest number is

(a) 60

(b) 65

(c) 67

(d) 72

**Answer:** (d) 72

Let the third number be x

∴ Second number = 3x

First number = 3x/2

A/Q | x + 3x + 3x/2 | = 44 |

3 |

⇒ x + 3x + 3x/2 = 44 X 3

⇒ | 2x + 6x + 3x | = 132 |

2 |

⇒ 11x = 132 X 2

⇒ x = 264/11 = 24

∴ Largest number = 3x = 3 X 24 = 72