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## Arithmetic: Averages Test-6

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Question 1 |

The average age of a group is increased by 5 years when a person of whose age is 33 yrs was replaced by a person whose age is 58. find the number of persons in the group?

4 | |

5 | |

8 | |

9 |

Question 1 Explanation:

Increase in the average = 5 years

Replaced person’s age = 33

The age of person who replaced = 58

So the number of persons in the group may be calculated as

New person age = Replaced person + (increase in average x number of terms)

Now we have the values

58 = 33 + (5n)

n = 5

so option b is the right answer

Let the number of members = n

Average = a

Total values will be = na

Now increase in average = 5 years

Therefore total new value = n(a +5)

Now na -33 + 58 = na +5n

na + 25 = na +5n = 5

Replaced person’s age = 33

The age of person who replaced = 58

So the number of persons in the group may be calculated as

New person age = Replaced person + (increase in average x number of terms)

Now we have the values

58 = 33 + (5n)

n = 5

so option b is the right answer

**Alternatively**Let the number of members = n

Average = a

Total values will be = na

Now increase in average = 5 years

Therefore total new value = n(a +5)

Now na -33 + 58 = na +5n

na + 25 = na +5n = 5

Question 2 |

The average height of 30 students is 140 cm .If 4 students whose average height was 90 cm leave the class find the average height of the remaining class

148 | |

142 | |

141 | |

150 |

Question 2 Explanation:

Average height = 140

Number of students = 30

Therefore total units are = 140 x 30 = 4200

Now the number of students who left the class = 4

And the average height of 4 students = 180

Therefore total units are 90 x 4 = 360

So the remaining units are 4200 – 360 = 3840 and the remained students are 26 = 148 cm

Number of students = 30

Therefore total units are = 140 x 30 = 4200

Now the number of students who left the class = 4

And the average height of 4 students = 180

Therefore total units are 90 x 4 = 360

So the remaining units are 4200 – 360 = 3840 and the remained students are 26 = 148 cm

Question 3 |

The average of 4 consecutive numbers is A then what will be the average of next 5 numbers of the series

4.5 | |

3.5 | |

4.8 | |

5.9 |

Question 3 Explanation:

Let the series of the consecutive numbers is x, x+1 , x+2 , x+3.

And the other five numbers would be = , x+4, x+5, x+6, x+7, x+8,

Now we are given by the average of first 4 numbers i.e. A

So A = {(4x +6)}/4

Therefore A = x + 1.5

Now we asked for the average of 5 next numbers so the next five numbers are

x+4, x+5, x+6, x+7, x+8, = 5x + 30

let us suppose the average is B

B = 5x + 30 /5 = x +6, which is equal to the A + 4.5

And the other five numbers would be = , x+4, x+5, x+6, x+7, x+8,

Now we are given by the average of first 4 numbers i.e. A

So A = {(4x +6)}/4

Therefore A = x + 1.5

Now we asked for the average of 5 next numbers so the next five numbers are

x+4, x+5, x+6, x+7, x+8, = 5x + 30

let us suppose the average is B

B = 5x + 30 /5 = x +6, which is equal to the A + 4.5

Question 4 |

The average monthly expenditure of Pranav in the first 7 months of a year is Rs. 3000. What should be his average monthly expenditure over the next months so that his average monthly expenditure over the year is Rs. 7000

13000 | |

18500 | |

12600 | |

16700 |

Question 4 Explanation:

Average monthly expenditure of Pranav in the first 7 months of a year = Rs. 3000

So total money would be = 21000

Months left five

Now his average monthly expenditure over the year should be Rs. 7000

So the total amount would be 7000 x 12 = 84000

So for next five months the salary would be = (84000 – 21000)/5 = 63000/5 = Rs. 12600

So total money would be = 21000

Months left five

Now his average monthly expenditure over the year should be Rs. 7000

So the total amount would be 7000 x 12 = 84000

So for next five months the salary would be = (84000 – 21000)/5 = 63000/5 = Rs. 12600

Question 5 |

The average age of 10 students in a class is 15 and if one teacher is added then the average increased by 2years .Find the age of the teacher

34 | |

25 | |

38 | |

37 |

Question 5 Explanation:

The number of students initially = 10

Average of ages = 15

So the total number of units = 150

Now one teacher is added the number of student and one teacher = 11

And the average is increased by 2 years

So new total units are = 11 x 17 = 187

So the age of the teacher = 187 – 150 = 37

Average of ages = 15

So the total number of units = 150

Now one teacher is added the number of student and one teacher = 11

And the average is increased by 2 years

So new total units are = 11 x 17 = 187

So the age of the teacher = 187 – 150 = 37

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