Average test 3-Solved questions with detailed explanations for SSC, IBPS, SBI PO, RRB, RBI, CSE, CGL, CHSL, CDA, CSE, UPSC

16)

The average of the ages of 4 workers is 23. Even if the age of the 5th worker is added, the average remains 23. What is the age of the 5th worker?

[Andhra Bank, 2009]

A)
32 yr
B)
21 yr
C)
23 yr
D)
Cannot be determined
E)
None of these

Answer: Option C

Explanation

Here we can use the formula

$Average (A)= \frac{Sum of observations (S)}{No . of observations (N)} ⇒ S=A×N$

According to the question,

Sum of 4 workers age (A=23, N=4)

⇒S=23 X 4 =92

Later, the age of 5th worker is added, the average remains 23. ( so A=23, N=5)

So, sum of 5 workers age

⇒S=23 X 5 =115

Now,

The age of 5th worker =(sum of 7 observations)-(Sum of 6 observations)

=115-92

=23 yr.

Hence, Option C is correct.

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Discussion

17)

The average height of 5 students is 162 cm. If the height of the 6th student is included, the average height increases by 1 cm. The height of the 6th student is?

[Corporation Bank, 2009]

A)
156 cm
B)
159 cm
C)
158 cm
D)
168 cm
E)
159.5 cm

Answer: Option D

Explanation

Here we can use the formula

$Average (A)= \frac{Sum of observations (S)}{No . of observations (N)} ⇒ S=A×N$

According to the question,

Sum of height of 5 students (A=162, N=5)

⇒S=162 X 5 =810

Later, height of the 6 th student is included, the average increases by 1 cm. (so A=163, N=6)

So, sum of height if 6 students

⇒S=163 X 6 =978

Now,

The height of 6th student =(sum of height of 5 students)-(Sum of height of 6 students)

=978-810

=168

Hence, Option D is correct.

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Discussion

18)

Th average age of 5 boys is 16 years, which that of 4 boys is 16yr 3months. The age of the 5th boy is?

A)
15 yr
B)
15 yr 6 months
C)
15 yr 4 months
D)
15 yr 2 months
E)
None of these

Answer: Option A

Explanation

Here we can use the formula

$Average (A)= \frac{Sum of observations (S)}{No . of observations (N)} ⇒ S=A×N$

According to the question,

Sum of 5 boys age (A=16, N=5)

⇒S=16 X 5 =80

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

So, sum of ages of 4 boys

⇒S=16.25 X 4 =65

Now,

Th age of 5th boy =(sum of 5 boys age)-(Sum of age of 4 boys)

=80-65

=15 yr.

Hence, Option A is correct.

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Discussion

19)

The mean wieght of a class of 35 students is 45 kg. If the wieght of the teacher be included, the mean weight increases by 500 g. Find the weight of the teacher?

A)
63 kg
B)
55 kg
C)
45 kg
D)
40 kg
E)
65 kg

Answer: Option A

Explanation

Here we can use the formula

$Average (A)= \frac{Sum of observations (S)}{No . of observations (N)} ⇒ S=A×N$

According to the question,

Sum of weight of 35 students (A=45, N=35)

⇒S=45 X 35 =1575

Later, wieght of the teacher included, the mean weight increases by 500 g. (so A=45.5, N=36)

So, sum of 35 students and a teacher is

⇒S=45.5 X 36 =1638

Now,

The weight of the teacher is =(sum of weight of 35 students)-(Sum of wieght of 35 students and a teacher is)

=1638-1575

=63 kg.

Hence, Option A is correct.

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Discussion

20)

The average marks scored by a student in 5 subjects is 40. After adding 6th subject, the average becomes 46. How many marks does the student score in his 6 th subject?

A)
80
B)
75
C)
50
D)
35
E)
None of these

Answer: Option B

Explanation

Here we can use the formula

$Average (A)= \frac{Sum of observations (S)}{No . of observations (N)} ⇒ S=A×N$

According to the question,

Sum of marks scored in 5 subjects (A=40, N=5)

⇒S=40 X 5 =200

Later, adding 6th subject , average becomes 46. (so A=46, N=6)

So, sum of score of 6 th subject

⇒S=46 X 6 =276

Now,

Student score in 6 th subject=(sum of score of 5 subjects)-(Sum of score of 6 subjects)

= 276-200

= 76

Hence, Option B is correct.

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Discussion

Average Test-3 (Addition or Elimination of Items)

Answer: Option C

Answer: Option D

Answer: Option A

Answer: Option A

Answer: Option B