# Averages Quiz Set 020

### Question 1

Each of the 8 girls of a class has a score 28 marks. If a new girl with a score 56 marks more than the average of all 9 girls is added, what is the sum total of the values of all 9 girls?

A

315 marks.

B

316 marks.

C

314 marks.

D

313 marks.

Soln.
Ans: a

Let the average of all 9 girls be x, then the required total is T = 9x. By averages, \$x = {8 × 28 + (x + 56)}/9\$ which is same as \$x × 9 = {8 × 28 + (x + 56)}\$, which is same as \$T = {8 × 28 + (T/9 + 56)}\$, solving for T we get 315 marks.

### Question 2

Average weight of a group of 25 boys is 46 Kg. Later it was found that the weighing machine was showing 3 Kg more than the actual weight. What is the actual average weight?

A

43.

B

44.

C

42.

D

41.

Soln.
Ans: a

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula \$46 = x/25\$, which gives x = \$46 × 25 = 1150\$. When weight of each of the 25 boys is reduced by 3 Kg, the new total becomes \$1150 - 25 × 3 = 1075\$, the new average becomes \$1075/25 = 43\$. TIP: As a shortcut, the new average = old average - error in weighing machine.

### Question 3

The average number of visitors at a zoo on a Monday is 72, whereas it is 108 on other days of the week. What will be the average number of visitors in a 30-day month that begins on a Monday?

A

102.

B

103.

C

101.

D

100.

Soln.
Ans: a

The month begins on a Monday, so there will be 5 Mondays. The average = \${5 × 72 + 25 × 108}/30\$, which equals \${360 + 2700}/30\$ = 102.

### Question 4

387 men and 258 women are employed in a farm. The average wage per person is Rs. 128. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 130.

B

Rs. 131.

C

Rs. 129.

D

Rs. 132.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 387 + (x - 5) × 258}/{387 + 258}\$ = 128. This equation can be solved for x to get Rs. 130 as the answer.

### Question 5

Average marks of class of 20 students is 85. What will be the average if each student is given 6 as grace marks?

A

91.

B

92.

C

90.

D

89.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula \$85 = x/20\$, which gives x = \$85 × 20 = 1700\$. When grace marks = 6 are added for each of the 20 students, the new total becomes \$1700 + 20 × 6 = 1820\$, the new average becomes \$1820/20 = 91\$. TIP: As a shortcut, the new average = old average + grace marks.