# CRE 1 - Simple Average | Average, Mixture & Alligation

**CRE 1 - Simple Average | Average, Mixture & Alligation**

The current average age of a family of five members is 37 years. Find the average age (in years) of the family after 3 years.

- A.
42

- B.
40

- C.
39

- D.
None of these

Answer: Option B

**Explanation** :

Since, age of every member of the family will increase by 3 years, the average of the whole family will also increase by 3 years.

Hence, option (b).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

The rainfall recorded in a city for the ten year period 1981 – 1990 is as follows (in cms):

89, 95, 70, 102, 29, 79, 63, 85, 72, 50

The mean rainfall is

- A.
bigger than 100

- B.
less than 100

- C.
between 95 and 100

- D.
less than 40

Answer: Option B

**Explanation** :

Mean rainfall = $\frac{\mathrm{89+95+70+102+29+79+63+85}}{10}$ = 73.4 cm

Hence, option (b).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

The population of six villages is 621, 679, 697, 603, 649 & 651. Find the average population of the villages.

- A.
649

- B.
650

- C.
672

- D.
691

Answer: Option B

**Explanation** :

Average = $\frac{621+679+697+603+649+651}{6}$ = 650

**Alternately,**

All these numbers are around 650.

Assume the base to be 650 and add the average deviation.

Average = Assumed average + average deviation

Average = 650 + $\frac{\left(621-650\right)+(679-650)+(697-650)+(603-650)+(649-650)+(651-650)}{6}$

Average = 650 + $\frac{-29+29+47-47-1+1}{6}$

Average = 650 + 0 = 650

Hence, option (b).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

The average temperature from Monday to Thursday was 48° and from Tuesday to Friday in the same week was 47°. If the temperature on Monday was 42°, find the temperature on Friday.

- A.
40°

- B.
38°

- C.
36°

- D.
34°

Answer: Option B

**Explanation** :

Given, Mon to Thur, (4 days) avg. Temp = 48°C

Thus, cumulative temp = 48 × 4 = 192°C.

Since temp, on Mon was 42°C

∴ Tue to Thur, (3 days), cumulative temp = 192 – 42 = 150°

Let temp. on Friday be x° C.

Then from the problem, (150 + x)/4 = 47

⇒ x = 38°C

Hence, option (b).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

The average of $32\frac{1}{3},32\frac{1}{4},31\frac{2}{3},33\frac{3}{4}$ is?

- A.
$32\frac{1}{2}$

- B.
32

- C.
$32\frac{1}{3}$

- D.
$32\frac{3}{4}$

- E.
$32\frac{2}{3}$

Answer: Option A

**Explanation** :

Sum of the numbers = $32\frac{1}{3}+32\frac{1}{4}+31\frac{2}{3}+33\frac{3}{4}$

= 32 + 32 + 31 + 33 + $\left[\frac{1}{3}+\frac{1}{4}+\frac{2}{3}+\frac{3}{4}\right]$

= 128 + $\left[\frac{1}{4}+\frac{3}{4}+\frac{1}{3}+\frac{2}{3}\right]$

= 128 + 2 = 130.

Average = $\frac{130}{4}$ = $32\frac{1}{2}$.

Hence, option (a).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

The average of 8 numbers is 23. If each of the numbers is multiplied by 8, find the average of the new set of numbers.

- A.
8

- B.
21

- C.
29

- D.
184

Answer: Option D

**Explanation** :

Cumulative score of 8 numbers = 8 × 23

New cumulative score = 8 × (8 × 23)

Avg. score of new set = (8 × 8 × 23)/8 = 184.

**Alternately,**

Since each number is multiplied with 8, the average also will become 8 times.

∴ New average = old average × 8 = 23 × 8 = 184.

Hence, option (d).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

Average of 8 consecutive odd natural numbers is 36. Find the highest of these 8 numbers.

Answer: 43

**Explanation** :

Let the first odd number be x.

∴ The numbers are: x, x + 2, x + 4, x + 6. x + 8, x + 10, x + 12 and x + 14.

Since these numbers are in Arithmetic Progression the average of these 8 numbers will be same as average of first and the last number.

∴ (x + x + 14)/2 = 36

⇒ 2x + 14 = 72

⇒ x = 29

∴ The highest number = x + 14 = 43.

**Alternately**,

Since consecutive odd numbers will be in Arithmetic Progression and there avereage is 36 which will also be the average of 4^{th} and 5^{th} numbers.

∴ The 4^{th} term will be 35 and 5^{th} will be 37. Now, the 6^{th} number will be 39, 7^{th} will be 41 and 8^{th} will be 43.

Hence, 43.

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

Average of 7 numbers is 25. When arranged in ascending order, average of the smallest 4 numbers is 15 and that of the largest 4 numbers is 36. Find the 4^{th} number?

- A.
28

- B.
29

- C.
30

- D.
31

Answer: Option B

**Explanation** :

The sum of all 7 numbers = 7 × 25 = 175

Average of the smallest 4 numbers = 4 × 15 = 60

Average of the largest 4 numbers = 4 × 36 = 144

⇒ Sum of all 7 numbers = Sum of smallest 4 numbers + Sum of largest 4 numbers - 4^{th} number

⇒ 175 = 60 + 144 - 4^{th} number

⇒ 4^{th} number = 204 - 175 = 29

Hence, option (b).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

Average of 9 numbers is 25. When arranged in ascending order, average of the smallest 4 numbers is 15 and that of the largest 4 numbers is 36. Find the 5^{th} number?

- A.
25

- B.
23

- C.
21

- D.
19

Answer: Option C

**Explanation** :

The sum of all 9 numbers = 9 × 25 = 225

Average of the smallest 4 numbers = 4 × 15 = 60

Average of the largest 4 numbers = 4 × 36 = 144

⇒ Sum of all 9 numbers = Sum of smallest 4 numbers + 5^{th} number + Sum of largest 4 numbers

⇒ 225 = 60 + 5^{th} number + 144

⇒ 5^{th} number = 225 - 204 = 21

Hence, option (c).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

What is the average of first 8 multiples of 4?

- A.
20

- B.
16

- C.
19

- D.
18

Answer: Option D

**Explanation** :

The first 8 multiples of 4 are: 4, 8, 12, ... and 32.

Sum of these numbers = 4 + 8 + 12 + ... + 32 = 4 × (1 + 2 + 3 + ... + 8) = 4 × 8 × 9/2 = 144

∴ Required average = 144/8 = 18

**Alternately**,

The first 8 multiples of 4 are: 4, 8, 12, ... and 32.

These numbers are in Arithmetic Progression, and average of numbers is AP is same as the average of first and the last numbers.

∴ Required average = (4 + 32)/2 = 18

Hence, option (d).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

5 years ago, the average age of a family of 4 was 21 years. A baby having been born, the average age of the family is same today. The present age of the baby is?

- A.
1

- B.
2

- C.
3

- D.
4

Answer: Option A

**Explanation** :

Total age of family of 4, 5 years ago = 4 × 21 = 84

Age of each member increases by 5 years, hence total increase should be 4 × 5 = 20 years.

∴ Total age of these 4 members of the family, at present = 84 + 20 = 104 years.

Total age of family of 5 (including the baby), today = 5 × 21 = 105

∴ Age of baby = Total age of 5 members - Total age of 4 original members.

= 105 - 104 = 1 year.

Hence, option (a).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

Average of all odd numbers from 1 to 30 is?

- A.
15.5

- B.
15

- C.
14

- D.
14.5

Answer: Option B

**Explanation** :

Odd numbers are 1, 3, 5, ..., 29.

These numbers are in AP, hence their average = (1 + 29)/2 = 15

Hence, option (b).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

Average of all even numbers from 1 to 30 is?

- A.
14

- B.
15

- C.
16

- D.
17

Answer: Option C

**Explanation** :

Even numbers are 2, 4, 6, ..., 30.

These numbers are in AP, hence their average = (2 + 30)/2 = 16

Hence, option (c).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

A batsman has an average of 30 runs in his 42 inning.The difference between his maximum and minimum score is 100. If these two innings are removed his average for 40 innings comes down to 28. What is his minimum score?

- A.
20

- B.
30

- C.
45

- D.
40

Answer: Option A

**Explanation** :

A batsman has an average of 30 runs in his 42 inning.The difference between his maximum and minimum score is 100. If these two innings are removed his average for 40 innings comes down to 28. What is his minimum score?

Total score of batsman across all 42 innings = 42 × 30 = 1260

Total score of batsman across 40 innings (excluding highest and lowest innings) = 40 × 28 = 1120

∴ Runs scored by him in the 2 innings with higest and lowest scores = 1260 - 1120 = 140

Let his score in lowest innings is x, hence his score in highest innings = x + 100

⇒ x + x + 100 = 140

⇒ x = 20

Hence, option (a).

Workspace:

**CRE 1 - Simple Average | Average, Mixture & Alligation**

Five years ago the average age of husband and wife was 23 years. Today the average age of husband, wife and child is 20 yrs. How old is child?

- A.
3 years

- B.
4 years

- C.
12 years

- D.
2 years

Answer: Option B

**Explanation** :

Five years ago the average age of husband and wife was 23 years. Today the average age of husband, wife and child is 20 yrs. How old is child?

Five years ago average of husband and wife = 23 years

Present average of husband and wife = 23 + 5 = 28 years

Present sum of the ages of husband and wife = 28 × 2 = 56.

Present sum of the ages of all 3 members = 20 × 3 = 60.

∴ Present age of the child = 60 - 56 = 4 years.

Hence, option (b).

Workspace:

## Feedback

Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.