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**Excercise 1**

1. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.

- 47.55 kg
- 48 kg
- 48.55 kg
- 49.25 kg

The Correct answer is :48.55 kg

Required average = $\left(\frac{50.25\times16+45.15\times8}{16+8}\right)$

= $\left(\frac{804+361.20}{24}\right)$

= $\frac{1165.20}{24}$

= 48.55

2. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:

- 10
- 20
- 40
- 73

The Correct answer is :40

Let there be x pupils in the class.

Total increase in marks =${(x\times\frac{1}{2}) = \frac{x}{2}}$

Therefore, ${\frac{x}{2}=(83-63)}$ => ${\frac{x}{2}=20}$

x=40

3. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:

- 53.33
- 54.68
- 55
- None of these

The Correct answer is :54.68

Required average=$\frac{\left(55\times50\right)+\left(60\times55\right)+\left(45\times60\right)}{55+60+45}$

=${(\frac{2750+3300+2700}{160})}$

= ${\frac{8750}{160}}$=54 .68

4. A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

- 250
- 276
- 280
- 285

The Correct answer is :285

Since the month begins with a Sunday, so there will be five Sundays in the month.

Required average = ${(\frac{510\times5+240\times25}{30})}$

= ${\frac{8550}{30}}$ = 285

5. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

- 35 years
- 40 years
- 50 years
- None of these

The Correct answer is :40 years

Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years

Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years

Therefore, Husband's present age = (90-50)years = 40 years

6. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

- 23 years
- 24 years
- 25 years
- None of these

The Correct answer is :23 years

Let the average age of the whole team by x years.

Therefore, 11x-(26+29) = 9(x-1)

11x - 9x=46)

=>2x = 46

=> x=23

So, the average age of the team is 23 years.

7. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

- 76 kg
- 76.5 kg
- 85 kg
- Data inadequate

The Correct answer is :85 kg

Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg

8. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

- 0
- 1
- 10
- 19

The Correct answer is :0

Average of 20 numbers = 0

Therefore Sum of 20 numbers (0 x 20) = 0

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a)

9. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

- Rs 4991
- Rs 5991
- Rs 6001
- Rs 6991

The Correct answer is :Rs 4991

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009

Therefore, required sale = Rs. [ (6500 x 6)-34009 ]

= Rs. (39000-34009)

=Rs. 4991

10. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

- 6.25
- 6.5
- 6.75
- 7

The Correct answer is :6.25

Required run rate = ${ \frac{282-(3.2\times 10)}{40} }$ = ${\frac{250}{40}}$ = 6.25

11. Average of all prime numbers between 30 to 50.

- 37
- 37.8
- 39
- 39.8

The Correct answer is :39.8

Prime numbers between 30 and 50 are: 31 ,37 ,41 ,43,47

Average of prime numbers between 30 to 50 will be

${\frac{31+37+41+43+47}{5}}$

${\frac{199}{5}}$= 39.8

12. Reeya obtained 65, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average.

- 70
- 75
- 80
- 85

13. Find the sum of first 30 natural numbers.

- 470
- 468
- 465
- 463

The Correct answer is :465

Sum of n natural numbers= ${\frac{n(n+1)}{2}}$

= ${\frac{30(30+1)}{2}}$

= ${ \frac{30(31)}{2}}$ = 465

14. Find the average of all numbers between 6 and 34 which are divisible by 5

- 15
- 20
- 25
- 30

The Correct answer is :20

Average = ${\frac{10+15+20+25+30}{5}}$

= ${\frac{100}{5}}$=20

15. Average of first five multiples of 3 is

- 9
- 11
- 13
- 15

The Correct answer is :9

Average= ${\frac{3(1+2+3+4+5)}{5}}$ =

= ${\frac{45}{5}}$=9

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