Average Test-3 (Addition or Elimination of Items)

Answer: Option C

Explanation

Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of 6 observations (A=12, N=6)

⇒S=12 X 6 =72

Later, Average decreased by 1 and number of observations increased by 1 (so A=11, N=7)

So, sum of 7 observations

⇒S=11 X 7 =77

Now,

7th observation=(sum of 7 observations)-(Sum of 6 observations)

therefore, 7th observation=77-72=5

Hence, Option C is correct.

Answer: Option D

Explanation

Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of runs in 10 innings (A=60, N=10)

⇒S=60 X 10 =600

Later, In how many runs are to be scored in the 11 innings to raise the mean score to 62 (so A=62, N=11)

So, sum of 7 observations

⇒S=62 X 11 =682

Now,

Score of 11th innings =(sum of runs in 10 innings)-(Sum of runs in 11 innings)

=682-600

= 82

Hence, Option D is correct.

Answer: Option B

Explanation

Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of weight of 34 students (A=42, N=34)

⇒S=42 X 34 =1428

Later, the weight of teacher included and the mean score rises by 400 g (so A=42.4, N=35)

So, sum of weight 35 students

⇒S=42.4 X 35 =1484

Now,

The weight of the teacher =(sum of weight 34 students)-(Sum of weight 35 students)

=1484-1428

=56 kg.

Hence, Option B is correct.

Answer: Option A

Explanation

Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of weight of 21 boys (A=64, N=21)

⇒S=64 X 21 =1344

Later, weight of the teacher added, the average increased by 1 kg. (so A=65, N=22)

So, sum of weight of 22

⇒S=65 X 22 =1430

Now,

Weight of the teacher =(sum of wieght of 21 boys)-(Sum of weight of 22 )

=1430-1344

= 86 kg.

Hence, Option A is correct.

Answer: Option C

Explanation

Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of 3 friends ages (A=23, N=3)

⇒S=23 X 3 =69

Later, if the age of 4th friend added, the average remains 23 (so A=23, N=4)

So, sum of 4 friends ages

⇒S=23 X 4 =92

Now,

Age of the 4th friend =(Sum of 3 friends ages)-(Sum of 4 friends ages)

= 92-69

= 23 yr.

Hence, Option C is correct.