__Average Questions for SSC/RRB Exams (03 – 04 – 2018)__**1. The average age of 18 boys and their teacher is 12 years. If the teacher’s age is excluded, the average age reduces by 3. What is the teacher’s age?**

a) 41 years

b) 51 years

c) 47 years

d) 66 years

**Explanation:**⇒ Given, average age of 18 boys and their teacher is 12 years

⇒ Average =
(sum of ages of boys and teacher)/(number of boys and teacher)

⇒ 12 = (sum
of ages of boys and teachers)/19

⇒ Sum of
ages of boys and teacher = 12 × 19 = 228 years

⇒ When
teacher’s age is excluded then average reduced by 3

⇒ New
average = 9

Average
= (sum of ages)/number

⇒ 9 = sum/18

⇒ sum of
ages of boys = 162 years

⇒ the age of
teacher = (228 - 162) years = 66 years

**2. The average score of a cricketer for ten matches is 38.9 runs. Find the average for the last four matches if the average for the first six matches is 42.**

a) 33.12

b) 23.65

c) 34.25

d) 30.74

**Answer: C)**

**Explanation:**Total score of last 4 matches = (10 × 38.9) – (6 × 42) = 389 – 252 = 137

Average
for last four matches = 137/4 = 34.25

**3. The average of five consecutive even numbers is 40. What is the value of smallest of these numbers?**

a) 35

b) 36

c) 44

d) 48

**Answer: B)**

**Explanation:**From the given data,

Let
us consider five consecutive even numbers be x, x + 2, x + 4, x + 6, x + 8

⇒ (x + x + 2
+ x + 4 + x + 6 + x + 8)/5 = 40

⇒ 5x + 20 =
200

⇒ 5x = 180

⇒ x = 180/5
= 36

∴ Smallest
of the numbers is 36

**4. The average of 7 numbers is 25. The average of 1st two numbers is 32.5 and average of next three numbers is 12.5. If the 6th number is 10.5 less than the 7th number, then find the last number.**

a) 18.5

b) 29

c) 31

d) 41.5

**Answer: D)**

**Explanation:**Average of 7 numbers = 25

Therefore,
sum of all 7 numbers = 7 × 25 = 175

Now,
Average of 1

^{st}two numbers = 32.5
Therefore,
Sum of 1

^{st}two numbers = 2 × 32.5 = 65
And,
Average of next 3 numbers = 12.5

Therefore,
Sum of next three numbers = 3 × 12.5 = 37.5

Hence,
Sum of last two numbers = 175 – (65 + 37.5) = 72.5

Let
the two numbers be X and Y.

∴ X + Y =
72.5

And,
X + 10.5 = Y

Solving,
we get,

X
= 31 and Y = 41.5

**5. If the sum of a few numbers is 480 and their mean is 32 and if another number 80 is included, the mean would become**

a) 35

b) 38

c) 40

d) 45

**Answer: A)**

**Explanation:**Mean = sum of observations/Number of observations

Given,
sum of a few numbers is 480 and their mean is 32

Total
no. of numbers taken = 480/32 = 15

Now,
another number 80 is included.

∴ Sum of
observations = 480 + 80 = 560

Mean
= 560/16 = 35

**6. The average of ten numbers is 45. If 5 is added to four numbers, the new average is**

a) 50

b) 45.5

c) 47

d) 49.5

**Answer: C)**

**Explanation:**Average of 10 numbers = 45

⇒ Sum of 10
numbers = 45 × 10 = 450

If
5 is added to four numbers:

Sum
of 10 numbers = 450 + 5 × 4 = 470

⇒ Average of
10 numbers = 470/10 = 47

∴ New
average = 47

**7. The average age of a 15-member cricket squad is 19 years, if the coach’s age is included, the average increase to 22 years. What is the coach’s age?**

a) 67 years

b) 52 years

c) 37 years

d) 44 years

**Answer: A)**

**Explanation:**Given, Average age of 15 members = 19

⇒ Sum of
ages of 15 members = 15 × 19 = 285

Given,
if the coach’s age is also included, we have average as 22 years.

⇒ (285 + Age
of coach)/16 = 22

⇒ 285 + Age
of coach = 16 × 22 = 352

⇒ Age of
coach = 352 – 285 = 67 years

**8. A batsman in his 12th innings makes a score of 79 runs and thereby increase his average score by 1. What is his average after the 12th innings?**

a) 71

b) 65

c) 67

d) 68

**Answer: D)**

**Explanation:**Let average score of first 11 innings be x runs.

Then,
total runs made by the batsman in 11 innings = 11x

According
to the question, after 12

^{th}inning, average score = x + 1
Therefore,
(79 + 11x)/12 = (x + 1)

⇒ 79 + 11x =
12x + 12

⇒ x = 79 – 12 = 67

Thus,
average score after 12

^{th}inning = 67 + 1 = 68 runs.**9. Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 63, then difference of first and third numbers is:**

a) 27

b) 50

c) 54

d) 48

**Answer: C)**

**Explanation:**Let the second number be x

∵ first
number is twice the second, the first number = 2x

Also,
since first number is half of the third, third number = 4x

Now,
the average of the 3 numbers is 63.

We
know that, average = Sum of all quantities/Number of quantities

∴ (2x + x
+4x)/3 = 63

⇒ 7x =189

⇒ x = 27

Thus,
the numbers are 54, 27 and 108

The
difference of first and third number = 108 – 54 = 54

**10. The average of 15 numbers is 35. If the mean of first 8 numbers is 33 and the mean of last 8 numbers is 37, what is the 8th number?**

a) 31

b) 23

c) 35

d) 41

**Answer: C)**

**Explanation:**Average = Sum of observations/No. of observations

∴ Sum of 15
numbers = Average × No.

⇒ Sum of 15
numbers = 35 × 15 = 525

⇒ Sum of
first 8 numbers = 33 × 8 = 264

⇒ Sum of
last 8 numbers = 37 × 8 = 296

Let
the 8

^{th}number be x
∴ x = (Sum
of first 8 no. + Sum of last 8 no.) – (Sum of 15
no.)

⇒ x = 264 +
296 – 525

⇒ x = 35