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**Excercise 2**

1. A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match

- 36
- 37
- 38
- 39

The Correct answer is :39

Let the average after 17th match is x

Then the average before 17th match is x-3

so 16(x-3) + 87= 17x

x=87 - 48 = 39

2. Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is

- 50
- 55
- 60
- 65

The Correct answer is :60

Total weight increased is $1.5\times10$ = 15

So weight of new person is 45 +15 = 60

3. Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is

- 35
- 45
- 55
- 65

The Correct answer is :35

Number is $\left(5\times27\right)- \left(4\times25\right)$ = 135-100 =35

4. The average score of a cricketer for ten matches is 38.9 runs. If the average for first six matches is 42, then average for last four matches is

- 33.25
- 32.25
- 34.25
- 34.5

The Correct answer is :34.25

Total runs scored in 10 matches = 10 x 38.9

Total runs scored in first 6 matches = 6 x 42

Total runs scored in the last 4 matches = (10 x 38.9) - (6 x 42) = 389 - 252 = 137

Average = $137\div4$ = 34.25

5. Average of 10 matches is 32, How many runs one should should score to increase his average by 4 runs.

- 70
- 76
- 78
- 80

The Correct answer is :76

Average after 11 innings should be 36

So, Required score = $\left(11\times36\right)-\left(10\times32\right)$

=>396-320 = 76

6. The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is z, then

- x = y + z
- 2x = y + z
- x = 2y + z
- x = y + 2z

The Correct answer is :2x = y + z

x = ${\frac{3y+3z}{6}}$ or 2x = y +z

7. When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students

- 55
- 56
- 57
- 58

The Correct answer is :57

Let the average weight of the 59 students be A.

Therefore, the total weight of the 59 of them will be 59 A.

The question states that when the weight of this student who left is added, the total weight of the class = 59A + 45.

When this student is also included, the average weight decreases by 0.2 kgs.

${\frac{59A+45}{60}}$ = A-0.2

=> 59A+45 = 60A-12

=> 45 + 12 = 60A-59A

=> A = 57

8. Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was :

- Rs 292.50
- Rs 297.50
- Rs298
- Rs 298.50

The Correct answer is :Rs 292.50

Let the average expenditure be Rs. x

Then, 9x = 8 x 30 + (x+20) or 9x = x + 260 or 8x = 260 or x = 32.50

Total money spent = 9x = Rs.(9 x 32.50) = Rs. 292.50

9. The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :

- 45 kg
- 46 kg
- 47 kg
- 48 kg

The Correct answer is :45 kg

Weight of the teacher=

$\left(35.4\times25-35\times24\right)$ kg = 45 kg

10. In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ?

- 8
- 9
- 10
- 11

The Correct answer is :11

Let the number of papers be x

Then, 63x+20+2 =65x or 2x=22 or x= 11

11. There are two sections A and B of a class, consisting of 36 and 44 studentsâ€™ respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.

- 30 kg
- 35 kg
- 42.5 kg
- 37.25 kg

The Correct answer is :37.25 kg

Total weight of (36+44) Students = ${36\times40+44\times35\frac{}{}}$ =2980 kg

Therefore average weight of the whole class =${\frac{2980}{80}}$ =37.25

12. The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :

- 6000
- 7000
- 8000
- 9000

The Correct answer is :9000

Let their prices be 3x, 5x and 7x.

Then 3x+5x+7x = 15000 x 3 or x =3000

Cost of cheapest item = 3x = Rs. 9000.

13. The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :

- 25
- 23
- 19
- 18

The Correct answer is :19

Sum of the present ages of husband, wife and child = $\left(23\times2+5\times2\right)+1$ = 57 years

Required average =${\frac{57}{3}}$=19 years

14. Of the three numbers, whose average is 60, the first is one-fourth of the sum of the others. The first number is :

- 17
- 29
- 36
- 48

The Correct answer is :36

The average of three numbers = 60

Therefore, sum of three numbers = $3\times60$ = 180

Let the sum of second and third be x

According to question, First number = x/4

Then, x+x/4 = 180

4x+x = $180\times4$

5x = 720

x = 720/5

x = 144

So, the first number = x/4 = 144/4 = 36

15. The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is :

- 11
- 12
- 13
- 14

The Correct answer is :11

Age of the 15th student = [15 x 15 - (14 x 5 + 16 x 9)] = 225 - 214 = 11 years

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