Average Test-3 (Addition or Elimination of Items)

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 runs scored in 15 innings (A=45, N=15)

⇒S=45 X 15 =675

Later, The runs average becomes 47, after 18 innings. (so A=47, N=18)

So, sum of runs scored in 18 innings

⇒S=47 X 18 =846

Now,

Runs scored in 20 innings =(sum of runs scored in 15 innings)-(Sum of runs scored in 18 innings)

=846-675

=171

Hence, Option B 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 cost of 49 pens and a pencil (A=63, N=50)

⇒S=63 X 50 =3150

Later, Cost of the pencil is removed, average drops down by 1. (so A=62, N=49)

So, sum of cost of 49 pens

⇒S=62 X 49 =3038

Now,

The cost of the pencil =(sum of cost of 49 pens and a pencil)-(Sum of cost of 49 pens)

=3150-3038

=112

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 height of 100 big trees and a banyan tree (A=3, N=101)

⇒S=3 X 101 =303

Later, Height of the banyan tree is not consider, the average decreases by 2 meters. (so A=1, N=100)

So, sum of 100 big trees

⇒S=1 X 100 =100

Now,

The height of banyan tree =(sum of 7 observations)-(Sum of 6 observations)

=303-100

=203

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 4 big book shelf and a small book shelf (A=120, N=5)

⇒S=120 X 5 =600

Later, the small book shelf are eliminated, the average deacreases by 50. (so A=70, N=4)

So, sum of 4 big book shelf

⇒S=70 X 4 =280

Now,

The number of books in small book shelf =(sum of 4 big book shelf and a small boook shelf)-(Sum of 4 big book shelf)

=600-280

=320

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 dresses 3 jute bags and a paper bag(A=60, N=4)

⇒S=60 X 4 =240

Later, the dresses of paper bag are eliminated, the average decreases by 10. (so A=50, N=3)

So, sum of dresses of 3 jute bags

⇒S=50 X 3 =150

Now,

The number of dresses in paper bag =(sum of dresses 3 jute bags and a paper bag)-(Sum of dresses 3 jute bags )

=240-150=90

Hence, Option D is correct.