# Averages Quiz Set 007

### Question 1

In a cricket match of 50 overs a team has to chase a target of 270 runs. During the first 10 overs it has scored at the rate of 3 runs per over. What is the required run rate for the remaining 40 overs?

A

6.

B

7.

C

5.

D

4.

Soln.
Ans: a

The runs already scored = scoring rate × overs = \$3 × 10\$ = 30. Required number of runs = 270 - 30 = 240 in 50 - 10 = 40 overs. Required rate = 240/40 = 6.

### Question 2

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 3

A box contains 5 marbles each having a weight of 66 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

91 grams.

B

92 grams.

C

90 grams.

D

89 grams.

Soln.
Ans: a

The weighted average = \${5 × 66 + 25 × 96}/30\$, which equals \${330 + 2400}/30\$ = 91.

### Question 4

370 men and 555 women are employed in a farm. The average wage per person is Rs. 97. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 100.

B

Rs. 101.

C

Rs. 99.

D

Rs. 102.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 370 + (x - 5) × 555}/{370 + 555}\$ = 97. This equation can be solved for x to get Rs. 100 as the answer.

### Question 5

There is a sequence of 60 consecutive odd numbers. The average of first 18 of them is 78. What is the average of all the 60 numbers?

A

120.

B

121.

C

119.

D

118.

Soln.
Ans: a

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is \${a + (a + (n-1) × 2)}/2\$ which is = a + n-1. We are given the average of first 18 terms as 78. So a + 18 - 1 = 78, which gives a = 61. The average of first 60 terms would be a + 60 - 1 = 61 + 60 - 1 = 120. 