# Averages Quiz Set 013

### Question 1

The average age of three friends 3 years ago was 31 years. The average age of two them 5 years ago was 19 years. What is the present age of the third friend?

A

54 years.

B

55 years.

C

53 years.

D

52 years.

Soln.
Ans: a

Let the present ages of the three friends be a, b and c. We are given \${(b - 5) + (c - 5)}/2\$ = 19. Which gives b + c = 48. We are also given \${(a - 3) + (b - 3) + (c - 3)}/3\$ = 31, which gives a + b + c = 3 * 31 + 9 = 102. Putting b + c here we get a = 102 - (b + c) = 102 - 48 = 54 years.

### Question 2

The average weight of the 12 bogies of a train increases by 9 Kg when a new bogie replaces a bogie of weight 12 Kg. What is the weight of the new bogie.

A

120.

B

121.

C

119.

D

122.

Soln.
Ans: a

The total increase of weight = 12 × 9 = 108. So the weight of the new bogie = 12 + 108 = 120 Kg.

### Question 3

What is the average of first 263 natural numbers?

A

132.

B

133.

C

131.

D

130.

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 = 263, we get average = 132.

### Question 4

Each of the 4 bulbs of a batch has a life 81 years. If a new bulb with a life 44 years more than the average of all 5 bulbs is added, what is the sum total of the values of all 5 bulbs?

A

460 years.

B

461 years.

C

459 years.

D

458 years.

Soln.
Ans: a

Let the average of all 5 bulbs be x, then the required total is T = 5x. By averages, \$x = {4 × 81 + (x + 44)}/5\$ which is same as \$x × 5 = {4 × 81 + (x + 44)}\$, which is same as \$T = {4 × 81 + (T/5 + 44)}\$, solving for T we get 460 years.

### Question 5

The sales(in rupees) of a karyana store for five consecutive days is 1770, 1086, 2220, 3774, 2154. What should be the sale on the sixth day so that the overall average sale is 1966?

A

Rs.792.

B

Rs.798.

C

Rs.786.

D

Rs.804.

Soln.
Ans: a

The total sale on first five days is 1770 + 1086 + 2220 + 3774 + 2154 = 11004. Let the sale on 6th day be x. The average for 6 days is: 1966 = \${11004 + x}/6\$ which gives x = \$6 × 1966 - 11004\$ = Rs. 792. 