# Problems on Average

Q21. The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years and that of the girls is 15.4 years. What is the ratio of boys to girls in the class ?

(a) 2 : 3

(b) 2 : 4

(c) 3 : 4

(d) 3 : 5

**Answer:** (a) 2 : 3

Let, the required ration be x : 1

∴ | (16.4 X x) + (15.4 X 1) | = 15.8 |

x + 1 |

⇒ 16.4x + 15.4 = 15.8x + 15.8

⇒ 16.4x - 15.8x = 15.8 - 15.4

⇒ 0.6x = 0.4

⇒ x = 0.4/0.6 = 2/3

∴ Ratio = 2/3 : 1 = 2 : 3

Q22. 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 B:1. If the average score of the boys is (A+1), the average score of the girls is

(a) A + 2

(b) A - 2

(c) A + 3

(d) A - 3

**Answer:** (d) A - 3

Let, the no. of boys be 3x and no. of girls be x

∴ Total no. of boys and girls = 3x + x = 4x

Total score = 4x.A

Total score of boys = 3x(A+1) = 3xA + 3x

Total score of girls = 4xA - (3xA + 3x) = xA - 3x

Average score of girls = (xA - 3x)/x = A - 3

Q23. The average of first 5 multiples of 5 is

(a) 10

(b) 15

(c) 20

(d) 25

**Answer:** (b) 15

First five multiples of 5's are 5, 10, 15, 20, 25

∴ Average = | 5 + 10 + 15 + 20 + 25 |

5 |

= | 75 |

5 |

= 15

Q24. The mean of 100 items was found to be 30. If at the time of calculation, two items were wrongly taken as 32 and 12 instead of 23 and 11, the correct mean is

(a) 29.90

(b) 31.32

(c) 32.50

(d) 33.45

**Answer:** (a) 29.90

sum of 100 items = 100 X 30 = 3000

Correct sum = (3000 - 12 - 32 + 23 + 11) = 2990

∴ Correct mean = 2990/100 = 29.90

Q25. If the total monthly income of 16 persons is Rs. 80800 and income of one of them is 120% of the average income, then his income is

(a) Rs. 5030

(b) Rs. 5075

(c) Rs. 6060

(d) Rs. 7025

**Answer:** (c) Rs. 6060

Required income = Rs. 120% of (80800/16)

= | 120 | X | 80800 |

100 | 16 |

= Rs. 6060

Q26. The average age of three boys is 16 years. If their ages are in the ratio 4:5:7, then the age of youngest boy is

(a) 10 years

(b) 12 years

(c) 14 years

(d) 15 years

**Answer:** (b) 12 years

Let, the ages of three boys be 4x, 5x, 7x

A/Q | 4x + 5x + 7x | = 16 |

3 |

⇒ 16x = 48

⇒ x = 48/16 = 3

∴ Age of youngest boy = 4 X 3 = 12 years

Q27. A man bought 4 shirts at Rs. 400 each, 4 pents at Rs. 300 each and 5 pairs of shoes at Rs. 500 each. What is the average expenditure per article ?

(a) Rs. 500

(b) Rs. 600

(c) Rs. 700

(d) Rs. 850

**Answer:** (b) Rs. 600

Total price of 4 shirts = Rs. 400 X 4 = Rs. 1600

Total price of 4 pents = Rs. 300 X 4 = Rs. 1200

Total price of 5 pairs of shoes = Rs. 500 X 10 = Rs. 5000

∴ Average expenditure = Rs. | 1600 + 1200 + 5000 | = Rs. | 7800 | = Rs. 600 |

4 + 4 + 5 | 13 |

Q28. The average height of the students in a class of 12 is 110 cm. If 18 more students with an average height of 115 cm join the class, what will be the new average height be ?

(a) 92 cm

(b) 95 cm

(c) 102 cm

(d) 113 cm

**Answer:** (d) 113 cm

Sum of the height of the 12 students = 12 X 110 cm = 1320 cm

Sum of the height of 18 students = 18 X 115 cm = 2070 cm

∴ Required average height = | 1320 + 2070 | cm = | 3390 | cm = 113 cm |

12 + 18 | 30 |

Q29. The average of five consecutive natural numbers is m. If the next three natural numbers are also included, how much more than m will the average of these 8 numbers be ?

(a) 1.5

(b) 1.7

(c) 1.8

(d) 2.1

**Answer:** (a) 1.5

Let five consecutive natural number be

n, n + 1, n + 2, n + 3, n + 4

∴ | n + (n + 1) + (n + 2) + (n + 3) + (n + 4) | = m |

5 |

⇒ | 5n + 10 | = m |

5 |

⇒ n + 2 = m

⇒ n = m - 2

∴ The numbers are m - 2, m - 1, m, m + 1, m + 2

The next three numbers are m + 3, m + 4, m + 5

∴ Average of 8 numbers be | (m - 2) + (m -1) + m + (m + 1) + (m + 2) + (m + 3) + (m + 4) + (m +5) |

8 |

= | 8m + 12 |

8 |

= | 8m | + | 12 |

8 | 8 |

= m + 1.5

Required number = 1.5

Q30. In an examination, a student's average marks were 55 per paper. If he had obtained 10 more marks for his Maths paper and 2 more marks for his Biology paper, his average per paper would have 57. How many papers were there in the examination.

(a) 5

(b) 6

(c) 7

(d) 8

**Answer:** (b) 6

Let the required number of paper be x

∴ Total marks of all papers = 55x

A/Q 57x - 55x = 10 + 2

⇒ 2x = 12

⇒ x = 6