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**Question 1:
**

The average of five numbers is 34.4. The average of the first and the second number is 46.5. The average of the fourth and the fifth number is 18. What is the third number ?

**a)**Ā 45

**b)**Ā 46

**c)**Ā 42

**d)**Ā 49

**e)**Ā None of these

**Question 2:
**

The average of five numbers is 56.4. The average of the first and the second number is 53. The average of the fourth and the fifth number is 56. What is the third number ?

**a)**Ā 63

**b)**Ā 62

**c)**Ā 67

**d)**Ā 68

**e)**Ā None of these.

QuestionĀ 3:

The average score of a cricketer for 13 matches is 42 runs. If his average score for the, first 5 matches is 54 runs, then what was his average score for the last 8 matches ?

**a)**Ā 37

**b)**Ā 39

**c)**Ā 34.5

**d)**Ā 33.5

**e)**Ā 37.5

Question 4:

The ratio between the ages of a father and his son four years ago was 19:6. If the difference between the ages of the father and son is 26 years. What will be the ratio of their present ages ?

**a)**Ā 21:8

**b)**Ā 23:8

**c)**Ā 23:10

**d)**Ā 27:14

**e)**Ā None of these

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**QuestionĀ 5:**

65% of a number is more than its 36% by 58. What is 23% of that number ?

**a)** 66

**b)** 69

**c)** 48

**d)** 46

**e)** None of these

**Question 6:**

Gaurav spends 40% of the amount he received from his father on hostel expenses, 20% on books and stationery and 50% of the remaining on transport. He saves Rs 450 which is half the remaining amount spending on hostel expenses,books etc.and transport. How much money did he get from his father ?

**a)**Ā Rs 3,000

**b)**Ā Rs 6,000

**c)**Ā Rs 4,500

**d)**Ā Canāt be determined

**e)**Ā None of these

**Solutions:Ā (1 toĀ 6)**

**1)**Ā Answer (e)

Average = total sum of elements /number of elements

Average of 5 numbers = 34.4

total of 5 numbers= 34.4 x 5 = 172

Similarly total sum of 1st and 2nd number = 46.5 x 2 = 93

Similarly total sum of 4th and 5th number = 18 x 2 = 36

3rd Number = 172 – (93+36) = 43

hence , E option is correct

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**2)**Ā Answer (e)

Average of 5 numbers is given as 56.4

Total of 5 numbers = Average x Number of Elements

Total of 5 numbers = 56.4 x 5 = 282

Average of 1st and 2nd number is 53

Total of 1st and 2nd number = 53 x 2 = 106

Average of 4th and 5th number is 56

total of 4th and 5th number = 56 x 2 = 112

1st + 2nd + 3rd +4th +5th = 282

106 + 3rd + 112 = 282

3rd = 64

hence option E is correct

**3)**Ā Answer (a)

Let the ages of the father and son be F and F-26.

Their ages four years ago are F-4 and F-30.

The ratio of these ages is 19:6

Therefore, (F-4)/(F-30) = 19/6

Or, 6F – 24 = 19F – 570

So, 13F = 546

Or, F = 42 and the age of the son is 42-26 = 16

Hence, the required ratio is 42:16 = 21:8

**4)** Answer (d)

Let the number be X

So, 0.65X – 0.36X = 58

Or, 0.29X = 58 and X = 200

Hence, 23% of X equals 0.23*200 = 46

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**5)**Ā Answer (c)

Let the money Gaurav inherited be equal to X

So, his hostel expenses equal 0.4X

Expenses on books and stationery is 0.2X

Remaining amount is X – 0.4X – 0.2X = 0.4X

Transport expenses is 50% of 0.4X = 0.2X

Remaining amount is 0.4X – 0.2X = 0.2X

He saves 50% of it, that is 0.1X and it equals 450.

So, the value of X is 450/0.1 = 4500

**6)**Ā Answer(c)

Let the money Gaurav inherited be equal to X

So, his hostel expenses equal 0.4X

ExpensesĀ on books and stationery is 0.2X

Remaining amount is X – 0.4X – 0.2X = 0.4X

Transport expenses is 50% of 0.4X = 0.2X

Remaining amount is 0.4X – 0.2X = 0.2X

He saves 50% of it, that is 0.1X and it equals 450.

So, the value of X is 450/0.1 = 4500

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**Instructions:
**

A city X has six villages around it. The population of village A is 25% of the population of city X while that of village B is 20% of that of city X. The population of village C is 2/5th of that of city X. The population of village D is 60% of that of village āC. The population of village E is 85% of that of village B. The population of village F is 21000 which is 35% of that of city X.

**Question 7:
**

What is the population of city X?

**a)**Ā 60000

**b)**Ā 80000

**c)**Ā 65000

**d)**Ā 64000

**e)**Ā None of these

Question 8:

Question 8:

The respecive ratio of between the population of village A and village D is

**a)**Ā 24 : 23

**b)**Ā 25 : 24

**c)**Ā 25 : 23

**d)**Ā 11 : 12

**e)**Ā None of these

Question 9:

Question 9:

The difference between the population of village C and village D is

**a)**Ā 9000

**b)**Ā 9500

**c)**Ā 9600

**d)**Ā 8800

**e)**Ā None of these

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**Question 10:**

By what per cent is the population of village E less than that of village A ?

**a)** 40%

**b)** 35%

**c)** 30%

**d)** 32%

**e)** None of these

**Solutions (7 to 10)**

7) Answer (a)

Population of city F = 21000

Population of city X = $$21000 \times \frac{100}{35} = 60000$$

**8)Ā AnswerĀ (b)
**LetĀ theĀ populationsĀ ofĀ villagesĀ X,A,B,C,D,E,FĀ beĀ x,a,b,c,d,e,fĀ respectively

GivenĀ that

aĀ =Ā 0.25x

b=0.2x

c=0.4x

d=0.6*0.4x=0.24

e=0.85*0.2x=0.17x

f=0.35x=21000

HeceĀ xĀ =Ā 60000

TheĀ respectiveĀ ratioĀ ofĀ betweenĀ theĀ populationĀ ofĀ villageĀ AĀ andĀ villageĀ DĀ =Ā a:dĀ =Ā 0.25x:0.24xĀ =Ā 25:24

**9)Ā AnswerĀ (c)
**LetĀ theĀ populationsĀ ofĀ villagesĀ X,A,B,C,D,E,FĀ beĀ x,a,b,c,d,e,fĀ respectively

GivenĀ that

aĀ =Ā 0.25x

b=0.2x

c=0.4x

d=0.6*0.4x=0.24x

e=0.85*0.2x=0.17x

f=0.35x=21000

HeceĀ xĀ =Ā 60000

TheĀ differenceĀ betweenĀ theĀ populationĀ ofĀ villageĀ CĀ andĀ villageĀ DĀ =Ā c-d

=0.4x-0.24xĀ =0.16x=0.16Ā xĀ 60000Ā =Ā 9600

**10)** Answer (d)

Let the populations of villages X,A,B,C,D,E,F be x,a,b,c,d,e,f respectively

Given that

a = 0.25x

b=0.2x

c=0.4x

d=0.6*0.4x=0.24x

e=0.85*0.2x=0.17x

f=0.35x=21000

Hece x = 60000

per cent by which the population of village Eis less than that of village A

= $$(0.25x-0.17x)/0.25x \times 100$$

=$$0.08/0.25 \times 100 $$

=32