# Averages Quiz Set 002

### Question 1

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 2

The average weight of 13 students of a class is 39 Kg, whereas the average weight of remaining 17 students is 30 Kg. What is the average weight of all 30 students?

A

\$33{9/10}\$.

B

\$35{2/29}\$.

C

\$32{25/31}\$.

D

\$36{9/28}\$.

Soln.
Ans: a

Total weight of 13 students is 13 × 39 = 507. Similarly, the total weight of remaining 17 students is 17 × 30 = 510. The total weight of all 30 students is 507 + 510 = 1017. So the average = 1017/30 = \$33{9/10}\$.

### Question 3

The average age of three friends 3 years ago was 30 years. The average age of two them 5 years ago was 13 years. What is the present age of the third friend?

A

63 years.

B

64 years.

C

62 years.

D

61 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\$ = 13. Which gives b + c = 36. We are also given \${(a - 3) + (b - 3) + (c - 3)}/3\$ = 30, which gives a + b + c = 3 * 30 + 9 = 99. Putting b + c here we get a = 99 - (b + c) = 99 - 36 = 63 years.

### Question 4

The sales(in rupees) of a karyana store for five consecutive days is 4392, 5040, 3630, 1554, 612. What should be the sale on the sixth day so that the overall average sale is 3179?

A

Rs.3846.

B

Rs.3852.

C

Rs.3840.

D

Rs.3858.

Soln.
Ans: a

The total sale on first five days is 4392 + 5040 + 3630 + 1554 + 612 = 15228. Let the sale on 6th day be x. The average for 6 days is: 3179 = \${15228 + x}/6\$ which gives x = \$6 × 3179 - 15228\$ = Rs. 3846.

### Question 5

Each of the 5 boys of a class has a weight 60 Kg. If a new boy with a weight 55 Kg more than the average of all 6 boys is added, what is the sum total of the values of all 6 boys?

A

426 Kg.

B

427 Kg.

C

425 Kg.

D

424 Kg.

Soln.
Ans: a

Let the average of all 6 boys be x, then the required total is T = 6x. By averages, \$x = {5 × 60 + (x + 55)}/6\$ which is same as \$x × 6 = {5 × 60 + (x + 55)}\$, which is same as \$T = {5 × 60 + (T/6 + 55)}\$, solving for T we get 426 Kg. 