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Problems on Average - (Page -1)

1. The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs.5200. What is the monthly income of A?

A. 2000 B. 3000 C. 4000 D. 5000

Explanation :

Let the monthly income of A = a

monthly income of B = b

monthly income of C = a

a +b=2×5050------------(Equation1)

b + c=2×6250------------(Equation2)

a +c=2×5200------------(Equation3)

(Equation 1) + (Equation 3) - (Equation 2)

=> ( a +b +a +c) “ (b +c)

=(2×5050)+(2×5200)”(2×6250)

=> 2a = 2(5050 + 5200 - 6250)

=> a = 4000

=> Monthly income of A = 4000

2.
In the first 10 overs of a cricket game, the run rate was only 3.2. What should
be the run rate in the remaining 40 overs to reach the target of 282 runs?

A.
6.25, B. 5.5, C. 7.4 , D. 5

**Answer : Option A**

Explanation
:

Runs
scored in the first 10 overs = 10×3.2=32

Total
runs = 282

remaining
runs to be scored = 282 - 32 = 250

remaining
overs = 40

Run
rate needed = 250/40=6.25

3.
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5
consecutive months. How much sale must he have in the sixth month so that he
gets an average sale of Rs.6500?

A.
4800 B. 4991
C. 5004 D. 5000

**Answer : Option B**

Explanation
: Let the sale in the sixth month = x

Then(
6435+6927+6855+7230+6562+x)/6=6500

=
> 6435 + 6927 + 6855+ 7230 + 6562 + x

=
6 × 6500 = 39000

=
> 34009 + x = 39000

=
> x = 39000 - 34009 = 4991

4.
The average of 20 numbers is zero. Of them, How many of them may be greater
than zero, at the most?

A.
1 B. 20 C. 0
D. 19

**Answer : Option D**

Explanation
: Average of 20 numbers = 0

=>Sum
of 20 numbers/20=0

=>
Sum of 20 numbers = 0

Hence
at the most, there can be 19 positive numbers.

(Such
that if the sum of these 19 positive numbers is x, 20th number will be -x)

5.
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older.
If the ages of these two are excluded, the
average age of the remaining players is one year
less than the average age of the whole team. Find
out the average age of the team.

A.
23 years B. 20 years C. 24 years
D. 21 years

**Answer : Option A**

Explanation
:Number of members in the team = 11

Let
the average age of the team = x

=>(Sum
of the ages of all the 11 members of the team)/11=x

=>
Sum of the ages of all the 11 members of the team = 11x

Age
of the captain = 26

Age
of the wicket keeper = 26 + 3 = 29

Sum
of the ages of 9 members of the team excluding captain and wicket keeper
= 11x - 26 - 29 = 11x - 55

Average
age of 9 members of the team excluding captain and
wicket keeper =(11x”55)/9

Given
that( 11x”55)/9=(x”1)

=>
11x - 55 = 9(x - 1)

=>
11x - 55 = 9x - 9

=>
2x = 46

=>x=46/2=23
years

6.
In Kiran’s opinion, his weight is greater than 65 kg but less than 72 kg. His
brother does not agree with Kiran and he thinks that Kiran’s weight is greater
than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be
greater than 68 kg. If all are them are correct in their estimation, what is
the average of different probable weights of Kiran?

A. 70 kg B. 69 kg C. 61 kg D. 67 kg

**Answer : Option D**

Explanation
: Let Kiran’s weight = x. Then

According
to Kiran, 65 < x < 72 ——————(equation 1)

According
to brother, 60 < x < 70 ——————(equation 2)

According
to mother, xd”68 ——————(equation3)

Given
that equation 1,equation 2 and equation 3 are correct. By combining these
equations, we can write as 65<xd”68

That
is x = 66 or 67 or 68

average
of different probable weights of Kiran = (66+67+68)/3=67

7.
The average weight of 16 boys in a class is 50.25 kg and that of the remaining
8 boys is 45.15 kg. Find the average weights of all the boys in the class.

A. 48.55
B. 42.25 C. 50
D. 51.25

**Answer : Option A**

Explanation
:

Average
weight of 16 boys = 50.25

Total
Weight of 16 boys = 50.25×16

Average
weight of remaining 8 boys = 45.15

Total
Weight of remaining 8 boys = 45.15×8

Total
weight of all boys in the class = (50.25×16)+(45.15×8)

Total
boys = 16+8=24

Average
weight of all the boys = (50.25×16)+(45.15×8)/24

=
(50.25×2)+(45.15×1)/3

=
(16.75×2) + 15.05

=33.5+15.05=48.55

=33.5+15.05=48.55

**(Continue....)**

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