# Averages Quiz Set 009

### Question 1

A box contains 5 marbles each having a weight of 144 grams. The box also contains 25 marbles each having a weight of 96 grams. What is the average weight of all the marbles in the box?

A

104 grams.

B

105 grams.

C

103 grams.

D

102 grams.

Soln.
Ans: a

The weighted average = \${5 × 144 + 25 × 96}/30\$, which equals \${720 + 2400}/30\$ = 104.

### Question 2

Average marks of class of 28 students is 51. What will be the average if each student is given 7 as grace marks?

A

58.

B

59.

C

57.

D

56.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula \$51 = x/28\$, which gives x = \$51 × 28 = 1428\$. When grace marks = 7 are added for each of the 28 students, the new total becomes \$1428 + 28 × 7 = 1624\$, the new average becomes \$1624/28 = 58\$. TIP: As a shortcut, the new average = old average + grace marks.

### Question 3

The average number of visitors at a zoo on a Monday is 138, whereas it is 84 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

93.

B

94.

C

92.

D

91.

Soln.
Ans: a

The month begins on a Monday, so there will be 5 Mondays. The average = \${5 × 138 + 25 × 84}/30\$, which equals \${690 + 2100}/30\$ = 93.

### Question 4

In a cricket match of 50 overs a team has to chase a target of 224 runs. During the first 30 overs it has scored at the rate of 4.8 runs per over. What is the required run rate for the remaining 20 overs?

A

4.

B

5.

C

3.

D

2.

Soln.
Ans: a

The runs already scored = scoring rate × overs = \$4.8 × 30\$ = 144. Required number of runs = 224 - 144 = 80 in 50 - 30 = 20 overs. Required rate = 80/20 = 4.

### Question 5

Average weight of a group of 8 boys is 89 Kg. Later it was found that the weighing machine was showing 4 Kg more than the actual weight. What is the actual average weight?

A

85.

B

86.

C

84.

D

83.

Soln.
Ans: a

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula \$89 = x/8\$, which gives x = \$89 × 8 = 712\$. When weight of each of the 8 boys is reduced by 4 Kg, the new total becomes \$712 - 8 × 4 = 680\$, the new average becomes \$680/8 = 85\$. TIP: As a shortcut, the new average = old average - error in weighing machine. 