# Problems on Average

# Important Formulas

Q1. Find the average of first 20 natural numbers ?

(a) 6

(b) 7.5

(c) 10.5

(d) 12

**Answer:** (c) 10.5

Sum of first n natural numbers = n (n + 1)/ 2

Sum of first 20 natural numbers = 20 (20 + 1)/ 2 = (20 X 21)/ 2 = 210

Average of first 20 natural numbers = 210 / 20 = 10.5

Q2. Total sale of a shop is 7770 Rs in a week. Find the
daily average sale of the store ?

(a) 111

(b) 1110

(c) 770

(d) 999

**Answer:** (b) 1110

Average = 7770 / 7 = 1110

Q3. The average monthly salry of 10 emplpyees is 3600 Rs.
If the salary of the manager is added then the average
salary is increased by 200 Rs. What is the monthly salary of
the manager ?

(a) 3700 Rs

(b) 4200 Rs

(c) 5800 Rs

(d) 6200 Rs

**Answer:** (c) 5800 Rs

Monthly Salary of Manager = (3800 X 11 - 3600 X 10) = 5800 Rs

Q4. The average of three odd number is 45. What is the
value of the highest number ?

(a) 33.3

(b) 42.3

(c) 45

(d) 47.5

**Answer:** (b) 42.3

Let the numbers be X, X + 2 and X + 6

So ((X + (X + 2) + (X + 6)) / 3 = 45

3X + 8 = 135

3X = 127

X = 42.3

Q5. A batsman in his 10th innings, makes a score of 72
runs and thereby increases his average score by 3 runs. What
will be the average after 10th innings ?

(a) 45

(b) 46

(c) 47

(d) 48

**Answer:** (a) 45

The average of the bastman till 9th innings = 72 - 10 X 3 = 42

So average after 10th innings = 42 + 3 = 45

Q6. A man covers half of his journey at 7 km/hr and the remaining half at 2 km/hr. His average speed is

(a) 2(1/2) km/hr

(b) 3(1/9) km/hr

(c) 4.5 km/hr

(d) 9 km/hr

**Answer:** (b) 3(1/9) km/hr

Average Speed = | 2xy | km/hr |

x+y |

= | 2 X 7 X 2 | km/hr |

7 + 2 |

= | 28 | km/hr |

9 |

= 3(1/9) km/hr

Q7. The average age of 11 palyers of a cricket team is decreased by 2 months when two of them aged 17 years and 20 years are replaced by two new players. The average age of the new players is

(a) 17y 7 months

(b) 19y 3 months

(c) 21y 9 months

(d) 23y 11 months

**Answer:** (a) 17y 7 months

Total age decreased = (2 X 11) months = 22 months = 1 year 10 months

Total age of two new players = (17 + 20) - 1 year 10 months = 37 y - 1y 10m = 35y 2 months

∴ Average age of the new players = (35y 2 months)/2 = 17y 7months

Q8. A man covers half of his journey at 6 km/h and the remaining half at 4 km/h. His average speed is

(a) 3.9 km./h

(b) 4.3 km/h

(c) 4.8 km/h

(d) 5.2 km/h

**Answer:** (c) 4.8 km/h

Average speed = | 2xy | km/h = | 2 X 6 X 4 | km/h = | 48 | km/h = 4.8 Km/h |

x + y | 6 + 4 | 10 |

Q9. There were 35 students in a hostel. If the number of students be increased by 7, the expenditure on food increases by Rs. 42 per day while the average expenditure of students is reduced by Rs. 1. What was the initial expenditure on food per day ?

(a) Rs. 375

(b) Rs. 390

(c) Rs. 420

(d) Rs. 460

**Answer:** (c) Rs. 420

Let, the initial expenditure be Rs. x

A/Q | x | - | (x + 42) | = 1 |

35 | 42 |

⇒ | 6x - 5(x + 42) | = 1 |

210 |

⇒ 6x - 5x - 210 = 210

⇒ x = 420

Q10. The average monthly salary of employees, consisting of officers and workers of an organisation is Rs. 3000. The average salary of an officer is Rs. 10000 while that of a worker is Rs. 2000 per month. If there are 400 employees in the organisation, the number of officers is

(a) 50

(b) 60

(c) 65

(d) 75

**Answer:** (a) 50

Let, the no. of officers be x

∴ No. of workers be (400 - x)

A/Q | x X 10000 + (400 - x) X 2000 | = 3000 |

400 |

⇒ 10000x + 800000 - 2000x = 3000 X 400

⇒ 8000x = 1200000 - 800000

⇒ x = 400000/8000 = 50