- 51. In a class of 18 students in an examination in science 1 student scored 100 marks, 2 get zero each and the average oh the rest was 45. What is the average of the whole class?

**Answer: Option 'B'**

**43**

- 52. In a class of 18 students in an examination in science 1 student scored 100 marks, 2 get zero each and the average oh the rest was 45. What is the average of the whole class?

**Answer: Option 'B'**

**43**

- 53. The average weight of 8 persons increases by 1.5kg when a person weighting 65kg is replaced by a new person. What could be the weight of the new person?

**Answer: Option 'D'**

**Let the average weight of 8 persons be 'x'
years and the age of the new person be 'y' years
so, (8x - 65 + y) / 8 = x+1.5
so, y = 77kgs
65 + 8X1.5 = 77kgs**

- 54. The average weight of 8 persons increases by 1.5kg when a person weighting 65kg is replaced by a new person. What could be the weight of the new person?

**Answer: Option 'D'**

**Let the average weight of 8 persons be 'x'
years and the age of the new person be 'y' years
so, (8x - 65 + y) / 8 = x+1.5
so, y = 77kgs
65 + 8X1.5 = 77kgs**

- 55. In a hostel of 12 boys and some girls, an average consumption of rice per month is 12 kg, while the Average consumption for boys is 16 kg per head and for girls 8 kg per head. The number of girls in The hostel?

**Answer: Option 'C'**

**Number of girls --- G
12+G) × 12 = (12 × 16)+(8 × G)
144 + 12G = 192 + 8G
12G − 8G = 192 − 144
4G = 48
G = 12.**

- 56. In a hostel of 12 boys and some girls, an average consumption of rice per month is 12 kg, while the Average consumption for boys is 16 kg per head and for girls 8 kg per head. The number of girls in The hostel?

**Answer: Option 'C'**

**Number of girls --- G
12+G) × 12 = (12 × 16)+(8 × G)
144 + 12G = 192 + 8G
12G − 8G = 192 − 144
4G = 48
G = 12.**

- 57. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

**Answer: Option 'B'**

**Given
The family consists of two grandparents, two parents and three grandchildren
The average age of two grandparents = 67 years.
=> **

- 58. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

**Answer: Option 'B'**

**Given
The family consists of two grandparents, two parents and three grandchildren
The average age of two grandparents = 67 years.
=> **

- 59. If 13:11 is the ratio of present age of Jothi and Viji respectively and 15:9 is the ratio between Jothi's age 4 years hence and Viji's age 4 years ago. Then what will be the ratio of Jothi's age 4 years ago and Viji's age 4 years hence?

**Answer: Option 'C'**

**Let the present age of Jothi and Viji be 13X and 11X respectively.
Given, Jothi's age 4 years hence and Viji's age 4 years ago in the ratio 15:9.
That is, (13X + 4) / (11X - 4) = 15 / 9
=> 9 (13X + 4) = 15 (11X - 4)
=> 117X + 36 = 165X - 60
=> 165X - 117X = 60 + 36
=> 48X = 96
=> X = 96 / 48
=> **

- 60. If 13:11 is the ratio of present age of Jothi and Viji respectively and 15:9 is the ratio between Jothi's age 4 years hence and Viji's age 4 years ago. Then what will be the ratio of Jothi's age 4 years ago and Viji's age 4 years hence?

**Answer: Option 'C'**

**Let the present age of Jothi and Viji be 13X and 11X respectively.
Given, Jothi's age 4 years hence and Viji's age 4 years ago in the ratio 15:9.
That is, (13X + 4) / (11X - 4) = 15 / 9
=> 9 (13X + 4) = 15 (11X - 4)
=> 117X + 36 = 165X - 60
=> 165X - 117X = 60 + 36
=> 48X = 96
=> X = 96 / 48
=> **

- 61. The average age of a group of 10 students was 14. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'A'**

**The average age of a group of 10 students is 14.
Therefore, the sum of the ages of all 10 of them = 10 * 14 = 140
When two students joins the group, the average increase by 1. New Average = 15
Now there are 12 students Therefore, sum of all the ages of 12 students = 15 x 12 = 180
Therefore, the sum of the ages of two students who joined = 180 - 140 = 40
And the average age of these two students = **

- 62. The average age of a group of 10 students was 14. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'A'**

**The average age of a group of 10 students is 14.
Therefore, the sum of the ages of all 10 of them = 10 * 14 = 140
When two students joins the group, the average increase by 1. New Average = 15
Now there are 12 students Therefore, sum of all the ages of 12 students = 15 x 12 = 180
Therefore, the sum of the ages of two students who joined = 180 - 140 = 40
And the average age of these two students = **

- 63. The average age of a group of 10 students was 14. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'A'**

**The average age of a group of 10 students is 14.
Therefore, the sum of the ages of all 10 of them = 10 * 14 = 140
When two students joins the group, the average increase by 1. New Average = 15
Now there are 12 students
Therefore, sum of all the ages of 12 students = ( 12 X 15 ) = 180
Therefore, the sum of the ages of two students who joined = 180 - 140 = 40
And the average age of these two students =**

- 64. The average age of a group of 10 students was 14. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'A'**

**The average age of a group of 10 students is 14.
Therefore, the sum of the ages of all 10 of them = 10 * 14 = 140
When two students joins the group, the average increase by 1. New Average = 15
Now there are 12 students
Therefore, sum of all the ages of 12 students = ( 12 X 15 ) = 180
Therefore, the sum of the ages of two students who joined = 180 - 140 = 40
And the average age of these two students =**

- 65. The average age of a group of 10 students was 24. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'A'**

**The average age of a group of 10 students is 24.
Therefore, the sum of the ages of all 10 of them = 10 × 24 = 240
When two students joins the group, the average increase by 1. New Average = 25
Now there are 12 students
Therefore, sum of all the ages of 12 students = ( 12 X 25 ) = 300
Therefore, the sum of the ages of two students who joined = 300 - 240 = 60
And the average age of these two students = **

- 66. The average age of a group of 10 students was 24. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'A'**

**The average age of a group of 10 students is 24.
Therefore, the sum of the ages of all 10 of them = 10 × 24 = 240
When two students joins the group, the average increase by 1. New Average = 25
Now there are 12 students
Therefore, sum of all the ages of 12 students = ( 12 X 25 ) = 300
Therefore, the sum of the ages of two students who joined = 300 - 240 = 60
And the average age of these two students = **

- 67. In the first 30 overs of a cricket game, the run rate was only 5. What should be the run rate in the remaining 20 overs to reach the target of 250 runs.?

**Answer: Option 'C'**

**Required Run rate = ( 250 - ( 5 x 30 ) ) / (20)
= ( 100) / (20)
**

- 68. In the first 30 overs of a cricket game, the run rate was only 5. What should be the run rate in the remaining 20 overs to reach the target of 250 runs.?

**Answer: Option 'C'**

**Required Run rate = ( 250 - ( 5 x 30 ) ) / (20)
= ( 100) / (20)
**

- 69. The average age of a group of 10 students was 16. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'B'**

**The average age of a group of 10 students is 16.
Therefore, the sum of the ages of all 10 of them
= 10 × 16 = 160
When two students joins the group, the average increase by 2.
New Average = 18
Now there are 12 students
Therefore, sum of all the ages of 12 students = 216
Therefore, the sum of the ages of two students who joined
= 216 - 160 = 56
And the average age of these two students
= 56 / 2
=**

- 70. The average age of a group of 10 students was 16. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'B'**

**The average age of a group of 10 students is 16.
Therefore, the sum of the ages of all 10 of them
= 10 × 16 = 160
When two students joins the group, the average increase by 2.
New Average = 18
Now there are 12 students
Therefore, sum of all the ages of 12 students = 216
Therefore, the sum of the ages of two students who joined
= 216 - 160 = 56
And the average age of these two students
= 56 / 2
=**

- 71. In the first 30 overs of a cricket game, the run rate was only 6.4. What should be the run rate in the remaining 20 overs to reach the target of 225 runs. ?

**Answer: Option 'A'**

**Required Run rate = ( 225 - ( 6.4 x 30 ) )/ (20) = ( 33) /(20) = 1.65**

- 72. In the first 30 overs of a cricket game, the run rate was only 6.4. What should be the run rate in the remaining 20 overs to reach the target of 225 runs. ?

**Answer: Option 'A'**

**Required Run rate = ( 225 - ( 6.4 x 30 ) )/ (20) = ( 33) /(20) = 1.65**

- 73. The average age of a group of 10 students was 22. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'C'**

**The average age of a group of 10 students is 22.
Therefore, the sum of the ages of all 10 of them = 10 * 22 = 220
When two students joins the group, the average increase by 1. New Average = 23
Now there are 12 students
Therefore, sum of all the ages of 12 students = 12 X 23 = 276
Therefore, the sum of the ages of two students who joined = 276 - 220 = 56
And the average age of these two students =**

- 74. The average age of a group of 10 students was 22. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?

**Answer: Option 'C'**

**The average age of a group of 10 students is 22.
Therefore, the sum of the ages of all 10 of them = 10 * 22 = 220
When two students joins the group, the average increase by 1. New Average = 23
Now there are 12 students
Therefore, sum of all the ages of 12 students = 12 X 23 = 276
Therefore, the sum of the ages of two students who joined = 276 - 220 = 56
And the average age of these two students =**

- 75. In the first 25 overs of a cricket game, the run rate was only 5.6. What should be the run rate in the remaining 25 overs to reach the target of 280 runs. ?

**Answer: Option 'D'**

**Required Run rate = ( 280 - ( 5.6 x 25 ) )/ (25) = ( 140) /(25) = 5.6**

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