Average - Aptitude MCQ Questions and Solutions with Explanations

According to the question,
Average weight of 25 students = 50 kg
Sum of the weight of 25 students
= 50 × 25 = 1250 kg
If the class teacher included the average is increased by 1 kg.
∴ Average weight of 25 students and teacher = 51 kg
∴ Sum of weight
= 26 × 51
= 1326 kg
∴ Class teacher weight
= 1326 - 1250
= 76 kg

Alternate :
If the weight of the class teacher is included the average is increased by 1 kg.
∴ Total increased in weight
= 26 × 1 = 26 kg
Note :
If the weight of class teacher is same as the average weight of 25 students then there would have been no effect on average. But the weight of class teacher is more than the average of 25 students weight then average is increased by 1 kg.
∴ Class teacher's weight
= 50 + 26 = 76 kg

According to the question,
Mean of 100 items is = 46
Sum of 100 items
= 46 × 100 = 4600
Misread 61 instead of 16 and 34 instead of 43
∴ Difference
= (61 + 34) - (16 + 43)
= 95 - 59
= 36 (more)
∴ Actual sum
= 4600 - 36
= 4564
Now total observations are = 90
∴ Actual average
= $$\frac{4564}{90}$$
= 50.7

Alternate :
Subtract the misread and add the correct from the sum.
Sum = 100 × 46 = 4600
New sum
= 4600 - (61 + 34) + (16 + 43)
= 4564
New number of observations = 90
New average = $$\frac{4564}{90}$$ = 50.7

Let the four even consecutive numbers
x, x + 2, x + 4, x + 6
According to the question,
$$\frac{{x + x + 2 + x + 4 + x + 6}}{4} = 15$$
4x + 12 = 60
4x = 48
x = 12
∴ 2^nd highest number is
= x + 4
= 12 + 4
= 16

99 × 99 + k = 100 × 100
k = 199

Alternate :
In 100^th innings average increased by 1
Runs scored in 100^th innings
= 100 × 1 + 99 = 199

Let the average of team is x
Then total score is 8x
But, According to question,
8x - 85 + 92 = 8 × 84
8x = 672 - 7
8x = 665

According to the question,
First six odd numbers which are divisible by '7'
7, 21, 35, 49, 63, 77
difference in each value is 14
Sn = $$\frac{n}{2}$$ [2a + (n - 1) d]
Sn = $$\frac{6}{2}$$ [2 × 7 + (6 - 1) × 14]
Sn = 3 (14 + 70)
Sn = 252
∴ Average = $$\frac{252}{6}$$ = 42

Let the average of runs for his 64 innings = x
∴ According to the question,
$$\frac{64x + 0}{65}$$   = x - 2
64x = 65x - 130
x = 130
∴ His new average is = 130 - 2 = 128

According to the question,
Average of whole class
$$\eqalign{ & = \frac{{10 \times 12.5 + 20 \times 13.1}}{{30}} \cr & = \frac{{125 + 262}}{{30}} \cr & = \frac{{387}}{{30}} \cr} $$
= 12.9 years

According to the question,
Correct average
$$\eqalign{ & = \frac{{5 \times 50 + 48 - 84}}{5} \cr & = \frac{{250 - 36}}{5} \cr & = \frac{{214}}{5} \cr} $$
= 42.8

Let us take 30 students average marks = x
Then,
30x + (3 × 85) = 60 × 65
x = 130 - 85
x = 45