Problems on Average with steps : Kerala PSC Degree Level Questions

  Problems on Average with steps : Kerala PSC Degree Level Questions

1. 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

2. 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

3. 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)

4. 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

5. 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

Answer : Option C

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

7. 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 ——————(equation

3) 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

8. 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

9. A library has an average of 510 visitors on Sundays

and 240 on other days. What is the average number

of visitors per day in a month of 30 days beginning

with a Sunday?

A. 290 B. 304 C. 285 D. 270

Answer : Option C

Explanation :in a month of 30 days beginning with

a Sunday, there will be 4 complete weeks and

another two days which will be Sunday and Monday

Hence there will be 5 Sundays and 25 other days in

a month of 30 days beginning with

a Sunday

Average visitors on Sundays = 510

Total visitors of 5 Sundays = 510×5

Average visitors on other days = 240

Total visitors of other 25 days = 240×25

Total visitors = (510×5)+(240×25)

Total days= 30

Average number of visitors per day ={ (510×5)

+ (240×25)}/30

= { (51×5)+(24×25) }/3

= (17×5) + (8×25)

=85+200=285

10. A student’s mark was wrongly entered as 83

instead of 63. Due to that the average marks for

the class got increased by half 1/2. What is the

number of students in the class?

A. 45 B. 40 C. 35 D. 30

Answer : Option B

Explanation : Let the total number of students =

x

The average marks increased by 1/2 due to

anincrease of 83-63=20 marks.

But total increase in the marks = 1/2×x=x/2

Hence we can write asx/2=20•Ëx=20×2=40