# PE 1 - Average | Average, Mixture & Alligation

**PE 1 - Average | Average, Mixture & Alligation**

If the average of 45, 67, 85, 42, 31 and x is 53, what is the value of x?

- A.
36

- B.
48

- C.
24

- D.
53

Answer: Option B

**Explanation** :

Average of given 6 numbers = 53 = (45+67+85+42+31+x)/6

⇒ 318 = 270 + x

⇒ x = 48

Hence, option (b).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

What is the arithmetic mean of the first ten prime numbers?

- A.
13.2

- B.
12.7

- C.
12.9

- D.
13

Answer: Option C

**Explanation** :

First ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Required average = (2+3+5+7+11+13+17+19+23+29)/10 = 12.9

Hence, option (c).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

The average weight of 11-member school cricket team, including the captain, is 83 kgs. The average weight decreases by 1 kg when the captain is not included. What is the captain’s weight?

- A.
93

- B.
83

- C.
73

- D.
72

Answer: Option A

**Explanation** :

Total weight of 11 members = 83 × 11 = 913 kgs.

Total weight excluding the captain = 82 × 10 = 820 kgs.

⇒ Weight of the captain = 913 – 820 = 93 kgs.

Hence, option (a).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

What is the average of the first 11 multiples of 9?

- A.
52

- B.
53

- C.
55

- D.
54

Answer: Option D

**Explanation** :

First 11 multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99.

Required average = (9 + 99)/2 = 54

Hence, option (d).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

If a group of four numbers, whose average is 60, the first is one-fifth the sum of the last three. What is the value of the first number?

- A.
47

- B.
43

- C.
40

- D.
60

Answer: Option C

**Explanation** :

Sum of the 4 numbers = 60 × 4 = 240

Let the sum of last three numbers be S.

∴ first number = S/5

⇒ S/5 + S = 240

⇒ 6S/5 = 240

⇒ S = 200

∴ 1st number = 200/5 = 40

Hence, option (c).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

The average of 15 numbers is 40. If 56 and 24 are discarded from this set, what is the average of the remaining numbers?

- A.
40

- B.
42

- C.
38

- D.
44

Answer: Option A

**Explanation** :

Sum of 15 numbers = 15 × 40 = 600

After discarding 56 and 24, sum of remaining 13 numbers = 600 – 56 – 24 = 520

⇒ Average of remaining 13 numbers = 520/13 = 40

Hence, option (a).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

What is the average of first 57 natural numbers?

- A.
28

- B.
28.5

- C.
29.5

- D.
29

Answer: Option D

**Explanation** :

Natural numbers are in Arithmetic Progression and average of number in AP is same as the average of first and the last term.

∴ Required average = (1 + 57)/2 = 29

Hence, option (d).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

The average age of a family of five is 27 years. The current age of the youngest member of the family, Rita, is 10 years. What was the average age of the family just before Rita’s birth?

- A.
31.25

- B.
30.5

- C.
21.25

- D.
27

Answer: Option C

**Explanation** :

Total age of 5 members = 27 × 5 = 135

Total age of 4 members excluding Rita = 135 – 10 = 125

Present average age of 4 members excluding Rita = 125/4 = 31.25

∴ Average age of 4 members 10 years ago = 31.25 – 10 = 21.25

Hence, option (c).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

A village has 1800 villagers, with an average height of 175 cm. The average height of the males is 178 cm; while that of the females is 170 cm. How many males does the village have?

- A.
1125

- B.
1250

- C.
675

- D.
1175

Answer: Option A

**Explanation** :

Let the number of males in the village = m.

⇒ $\frac{178m+170(1800-m)}{1800}$ = 175

⇒ 178m + 170 × 1800 – 170m = 175 × 1800

⇒ 8m = 175 × 1800 – 170 × 1800

⇒ 8m = 5 × 1800

⇒ m = 1125

Hence, option (a).

Workspace:

**PE 1 - Average | Average, Mixture & Alligation**

Of the 7 numbers, average of first 4 numbers is 25 while that of the last 4 numbers is 31. Average of all 7 numbers is 28. Find the 4th number.

- A.
28

- B.
27

- C.
29

- D.
30

Answer: Option A

**Explanation** :

Sum of all the 7 numbers = 28 × 7 = 196

Sum of first 4 numbers = 25 × 4 = 100

Sum of last 4 numbers = 31 × 4 = 124

⇒ Sum of first 4 numbers + sum of last 4 numbers – 4^{th} number = Sum of all 7 numbers.

⇒ 100 + 124 – 4^{th} number = 196

⇒ 4^{th} number = 224 – 203 = 28.

Hence, option (a).

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