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1. The average age of a class of 30 students and a teacher reduces by 0.5 years on excluding the age of teacher. If the average age is 14 years, find the age of the class teacher.

A. 36 years

B. 30 years

C. 29 years

D. 15 years

**Answer : ****29 years**

Age of teacher = Total age of (students + teacher) - Total age of students

= 31 x 14 - 30 x 13.5

= 434 - 405 = 29 years

Another approach:

Since the average falls 0.5 less when the teacher is excluded from the team, he has to give 0.5 years to the age of each of the 30 students. Hence, he has 30 x 0.5 = 15 years to give over and above maintaining his own average age of 14 years.

So, Age of the teacher = 14 + 15 = 29 years

2. In June, a baseball team which played 60 games, won 30% of its games played. After a phenomenal winning streak, this team raised its average to 50%. How many games must the team have won in order to attain this average?

A. 18

B. 20

C. 24

D. 26

**Answer : ****24**

If the team won 30% of 60 games then it won 18 games out of 60.

In order to attain 50%, the additional games must be played by the team will be,

(18 + x ) / (60 + x) = 50/100

By solving, x = 24 (Additional games must be played).

3. At present, the average age of father and son is 29 years. The average age of father, mother and son five years from now will be 37 years. Find the mother’s present age.

A. 38 years

B. 40 years

C. 41 years

D. 46 years

**Answer : ****38 years**

Let Father’s age = F, Son’s age = S, Mother’s age = M

At present, (F+S) / 2 = 29

F+S = 58

From the problem statement, the average age of Father, Son and Mother is given 5 years from now. So, each of them will have 5 years more than the present age.

(F+5+S+5+M+5) / 3 = 37

((F+S+M) + 15 ) / 3 = 37

F+S+M = 96

Substituting F+S = 58, M = 38.

4. The average scores of a cricketer from certain number of innings is 15. When he plays one more inning, and scores a duck his average drops to 13.5. How many innings has he played in total including the latest one?

A. 12

B. 11

C. 10

D. 9

**Answer : ****10**

Average = Total runs / innings

Total runs / innings = 15 (Given)

In the latest innings, he scores duck (0) then the total runs will remain same.

After playing latest innings the average is 13.5

Total runs / (innings+1) = 13.5

Solving the above two equations, innings = 9.

The total innings including the latest one = 9 + 1 = 10.

5. A shipping clerk has five boxes of different and unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs first and second, second and third and so on. The weights so obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?

A. 60 kg

B. 62 kg

C. 64 kg

D. 68 kg

**Answer : ****62 kg**

From the options,

The highest weight of 60 can not be because to arrive at a total of 121, the other box will have to weigh 61 kg which will then become the highest. The highest weight of 64 is wrong too, because to add up to 121, the other weight will have to be 57 and to make up to a total of 120, the next box shall have a weight 63 which obviously makes the maximum possible total as 64 + 63 = 127.

The highest weight of 62 is the correct answer because the other boxes shall be 59, 54, 58, 56. These will give all the totals given above.

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