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- 16. In Madan's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Madan and he thinks that Madan'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 Madan?

A.68 kg

B.69 kg

C.67 kg

D.70 kg

Answer & Explanation

Answer: Option C

Explanation:**Let Madan's weight = x. Then**

According to Madan, 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

i.e., x = 66 or 67 or 68

Average of different probable weights of Madan = (66+67+68)/3 = 67

According to Madan, 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

i.e., x = 66 or 67 or 68

Average of different probable weights of Madan = (66+67+68)/3 = 67

- 17. A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class?

A.45

B.40

C.35

D.38

Answer & Explanation

Answer: Option B

Explanation:**Let the total number of students = x**

The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks.

But total increase in the marks = 1/2 × x = x/2

Hence we can write as

x/2 = 20

⇒ x = 20 × 2 = 40

The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks.

But total increase in the marks = 1/2 × x = x/2

Hence we can write as

x/2 = 20

⇒ x = 20 × 2 = 40

- 18. The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. How many workers are there in the workshop?

A.21

B.23

C.27

D.31

Answer & Explanation

Answer: Option A

Explanation:**Let the number of workers = x**

Given that average salary of all the workers = Rs.8000

Then, total salary of all workers = 8000x

Given that average salary of 7 technicians is Rs.12000

=> Total salary of 7 technicians = 7 × 12000 = 84000

Count of the rest of the employees = (x - 7)

Average salary

Given that average salary of all the workers = Rs.8000

Then, total salary of all workers = 8000x

Given that average salary of 7 technicians is Rs.12000

=> Total salary of 7 technicians = 7 × 12000 = 84000

Count of the rest of the employees = (x - 7)

Average salary

**of**

**the rest of the employees = Rs.6000**

Total salary of the rest of the employees = (x - 7)(6000)

8000x = 84000 + (x - 7)(6000)

=> 8x = 84 + (x - 7)(6)

=> 8x = 84 + 6x - 42

=> 2x = 42

=> x = 42/2 = 21

Total salary of the rest of the employees = (x - 7)(6000)

8000x = 84000 + (x - 7)(6000)

=> 8x = 84 + (x - 7)(6)

=> 8x = 84 + 6x - 42

=> 2x = 42

=> x = 42/2 = 21

- 19. In an examination, a student's average marks were 63. If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65. How many subjects were there in the examination?

A.12

B.13

C.11

D.15

Answer & Explanation

Answer: Option C

Explanation:**Let the number of subjects = x**

Then, total marks he scored for all subjects = 63x

If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65

=> Total marks he would have scored for all subjects = 65x

Now we can form the equation as 65x - 63x = additional marks of the student = 20 + 2 = 22

=> 2x = 22

=> x = 22/2 = 11

Then, total marks he scored for all subjects = 63x

If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65

=> Total marks he would have scored for all subjects = 65x

Now we can form the equation as 65x - 63x = additional marks of the student = 20 + 2 = 22

=> 2x = 22

=> x = 22/2 = 11

- 20. The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year old child. What is the average age of the family ?

A.19 years

B.26 years

C.27 years

D.29 years

Answer & Explanation

Answer: Option A

Explanation:**Total age of husband and wife (at the time of their marriage) = 2 × 23 = 46**

Total age of husband and wife after 5 years + Age of the 1 year old child

= 46 + 5 + 5 + 1 = 57

Average age of the family = 57/3 = 19

Total age of husband and wife after 5 years + Age of the 1 year old child

= 46 + 5 + 5 + 1 = 57

Average age of the family = 57/3 = 19

**To whom this Averages Questions and Answers section is beneficial?**

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