Brief Notes on Average With Quiz
TIPS FOR SOLVING QUESTIONS RELATED
TO AVERAGE:
1. The average of a number of
quantities of the same kind is equal to their sum divided by the number of
those quantities. Thus,
Average = Sum of the
quantities / Number of quantities
Also, Sum of the quantities =
Average x Number of quantities.
2. If a man covers a certain
distance at x km/h and an equal distance at y km/h.
Then, the average speed during the
whole journey is given by
2xy/x+y km/h
1. 10 students started to eat
biscuits. Among them, 1 ate 8 biscuits, 2 of them ate 6 biscuits each, 3 of
them ate 4 biscuits each and 4 of them ate 2 biscuits each. The average number
of biscuits, each of them ate, was:
A. 4
B. 6
C. 8
D. 3
2. The mean of 11 numbers is 35. If
the mean of first 6 numbers is 32 and that of the last 6 numbers is 37, find
the sixth number.
A. 27
B. 28
C. 29
D. 30
3. In a 20 over match, the required
run rate to win is 7.2. If the run rate is 6 at the end of the 15th over, the
required run rate to win the match is:
A. 1.2
B. 13.2
C. 10.8
D. 12
4. The average of 9 integers
arranged in a certain order is 32. If the average of the first four integers is
26 and that of the last four integers is 28, then the fifth integer is:
A. 76
B. 72
C. 68
D. 58
5. A batsman has a certain average
of runs for 11 innings. In the 12th innings, he makes a score of 90 runs,
thereby increasing his average by 5. His average after the 12th innings is:
A. 30
B. 35
C. 40
D. 45
6.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
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
8.A family consists of two
grandparents, two parents and three grandchildren. The average age of the
grandparents is 67 years, that of the parents is 35 years and that of the
grandchildren is 6 years. What is the average age of the family?
A. 28 4/7 years
B. 31 5/7 years
C. 32 1/7 years
D. None of these
9. If the average marks of three
batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the
average marks of all the students?
A. 53.23
B. 54.68
C. 51.33
D. 50
10.A student needed to find the
arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He
found the mean to be 12. What is the value of x?
A. 12
B. 5
C. 7
D. 9
ANSWER AND SOLUTION :
1(A)Explanation:
Total number of biscuits = 1*8+2*6+3*4+4*2= 8 + 12 + 12 + 8 = 40
Average number of biscuits = 40/10= 4
2(C)Explanation:
The sixth number = 6*32 + 6 * 37-11*35
= 192 + 222 - 385
= 29
3(C)Explanation:
Total runs required to win the match = 20 * 7.2 = 144
Runs scored in 15 over = 15 * 6 = 90
Runs required in 5 overs = 144 - 90 = 54
Required run rate = 54/5 = 10.8
4(B)Explanation:
Fifth integer = 9*32 - 4*26 - 4*8
= 288 - 104 - 112
= 72
5(B)Explanation:
Let avrage run of 1 innings = x
Total runs of 11 innings = 11x
Score of 12th innings = 90
Average run of 12 innings = x=5
Total runs of 12 innings = 12(x+5)
12(x+5) - 11x = 90
12x + 60 - 11x = 90
x = 30
Thus, average run after the 12th innings = 30+5= 35
6(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 (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, x = 68 ------------(equation 3)
Given that equation 1,equation 2 and equation 3 are correct. By combining these equations,
we can write as
65<x=68
That is x = 66 or 67 or 68
average of different probable weights of Kiran = (66+67+68)/3=67
8( B)Explanation:
Required average = (67 x 2 + 35 x 2 + 6 x 3)/(2+2+3)
= (134 + 70 + 18)/7
= 222/7
= 31 5/7 years.
9(B)Explanation :
Average marks of batch1 = 50
Students in batch1 = 55
Total marks of batch1=55×50
Average marks of batch2 = 55
Students in batch2 = 60
Total marks of batch2=60×55
Average marks of batch3 = 60
Students in batch3 = 45
Total marks of batch3=45×60
Total students = 55 + 60 + 45 = 160
Average marks of all the students = ((55×50)+(60×55)+(45×60))/160
=(275+330+270)/16 = 875/16=54.68
10(C)Explanation :
(3+11+7+9+15+13+8+19+17+21+14+x)/12 =12
=>137+x/12=12
=> 137 + x = 144
=> x = 144 - 137 = 7
ANSWER AND SOLUTION :
1(A)Explanation:
Total number of biscuits = 1*8+2*6+3*4+4*2= 8 + 12 + 12 + 8 = 40
Average number of biscuits = 40/10= 4
2(C)Explanation:
The sixth number = 6*32 + 6 * 37-11*35
= 192 + 222 - 385
= 29
3(C)Explanation:
Total runs required to win the match = 20 * 7.2 = 144
Runs scored in 15 over = 15 * 6 = 90
Runs required in 5 overs = 144 - 90 = 54
Required run rate = 54/5 = 10.8
4(B)Explanation:
Fifth integer = 9*32 - 4*26 - 4*8
= 288 - 104 - 112
= 72
5(B)Explanation:
Let avrage run of 1 innings = x
Total runs of 11 innings = 11x
Score of 12th innings = 90
Average run of 12 innings = x=5
Total runs of 12 innings = 12(x+5)
12(x+5) - 11x = 90
12x + 60 - 11x = 90
x = 30
Thus, average run after the 12th innings = 30+5= 35
6(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 (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, x = 68 ------------(equation 3)
Given that equation 1,equation 2 and equation 3 are correct. By combining these equations,
we can write as
65<x=68
That is x = 66 or 67 or 68
average of different probable weights of Kiran = (66+67+68)/3=67
8( B)Explanation:
Required average = (67 x 2 + 35 x 2 + 6 x 3)/(2+2+3)
= (134 + 70 + 18)/7
= 222/7
= 31 5/7 years.
9(B)Explanation :
Average marks of batch1 = 50
Students in batch1 = 55
Total marks of batch1=55×50
Average marks of batch2 = 55
Students in batch2 = 60
Total marks of batch2=60×55
Average marks of batch3 = 60
Students in batch3 = 45
Total marks of batch3=45×60
Total students = 55 + 60 + 45 = 160
Average marks of all the students = ((55×50)+(60×55)+(45×60))/160
=(275+330+270)/16 = 875/16=54.68
10(C)Explanation :
(3+11+7+9+15+13+8+19+17+21+14+x)/12 =12
=>137+x/12=12
=> 137 + x = 144
=> x = 144 - 137 = 7
