CRE 1 - Simple Average | Average, Mixture & Alligation

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).

Answer: Option B

Explanation :

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

Hence, option (b).

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).

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).

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).

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).

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.

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).

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).

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).

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).

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).

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).

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).

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).