# Averages Quiz Set 006

### Question 1

Two of the 32 numbers are 32 and 42, If these two are excluded the average of the remaining 30 numbers is 1 less than the average of all the 32 numbers. What is the average of all the 32 numbers?

A

22.

B

23.

C

21.

D

24.

Soln.
Ans: a

Let the required average be x. Then \$32x - (32 + 42) = 30 × (x - 1).\$ which gives \$32x - 74 = 30 × (x - 1).\$ Solving for x we get x = 22.

### Question 2

What is the average of first 275 natural numbers?

A

138.

B

139.

C

137.

D

136.

Soln.
Ans: a

The sum of first n natural numbers is \$(n × (n + 1))/2\$. The average is \${(n × (n + 1))/2}/n\$ which is \$(n + 1)/2.\$ Putting n = 275, we get average = 138.

### Question 3

There are three sections in school with 40, 40 and 40 students respectively. The average weight of a student in these sections, respectively, is 3, 3 and 2 Kg. What is the average weight of all the the students of the combined sections?

A

\$2{2/3}\$.

B

\$2{27/40}\$.

C

\$2{79/120}\$.

D

\$2{13/20}\$.

Soln.
Ans: a

The sums of the weights of all the students is 40 × 3 + 40 × 3 + 40 × 2 = 320. The required average = 320/total students = \$320/{40 + 40 + 40}\$ = \${8/3}\$, which is same as: \$2{2/3}\$.

### Question 4

306 men and 204 women are employed in a farm. The average wage per person is Rs. 168. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 170.

B

Rs. 171.

C

Rs. 169.

D

Rs. 172.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 306 + (x - 5) × 204}/{306 + 204}\$ = 168. This equation can be solved for x to get Rs. 170 as the answer.

### Question 5

The average number of visitors at a zoo on a Monday is 156, whereas it is 162 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

161.

B

162.

C

160.

D

159.

Soln.
Ans: a

The month begins on a Monday, so there will be 5 Mondays. The average = \${5 × 156 + 25 × 162}/30\$, which equals \${780 + 4050}/30\$ = 161. 