# Averages Quiz Set 016

### Question 1

There are three sections in school with 20, 40 and 30 students respectively. The average weight of a student in these sections, respectively, is 2, 5 and 2 Kg. What is the average weight of all the the students of the combined sections?

A

\$3{1/3}\$.

B

\$3{31/90}\$.

C

\$3{29/90}\$.

D

\$3{14/45}\$.

Soln.
Ans: a

The sums of the weights of all the students is 20 × 2 + 40 × 5 + 30 × 2 = 300. The required average = 300/total students = \$300/{20 + 40 + 30}\$ = \${10/3}\$, which is same as: \$3{1/3}\$.

### Question 2

The average age of three friends 3 years ago was 33 years. The average age of two them 5 years ago was 19 years. What is the present age of the third friend?

A

60 years.

B

61 years.

C

59 years.

D

58 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\$ = 33, which gives a + b + c = 3 * 33 + 9 = 108. Putting b + c here we get a = 108 - (b + c) = 108 - 48 = 60 years.

### Question 3

The average age of three friends 3 years ago was 31 years. The average age of two them 5 years ago was 12 years. What is the present age of the third friend?

A

68 years.

B

69 years.

C

67 years.

D

66 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\$ = 12. Which gives b + c = 34. 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 - 34 = 68 years.

### Question 4

The sales(in rupees) of a gift shop for six consecutive days is 3594, 4422, 1800, 2724, 732 and 4164. What is the overall average sale for these six days?

A

Rs.2906.

B

Rs.2912.

C

Rs.2900.

D

Rs.2918.

Soln.
Ans: a

The total sale on first six days is 3594 + 4422 + 1800 + 2724 + 732 + 4164 = 17436. The average for 6 days is: 17436/6, which gives Rs. 2906.

### Question 5

The average weight of 19 students of a class is 39 Kg, whereas the average weight of remaining 12 students is 38 Kg. What is the average weight of all 31 students?

A

\$38{19/31}\$.

B

\$39{9/10}\$.

C

\$37{13/32}\$.

D

\$41{8/29}\$.

Soln.
Ans: a

Total weight of 19 students is 19 × 39 = 741. Similarly, the total weight of remaining 12 students is 12 × 38 = 456. The total weight of all 31 students is 741 + 456 = 1197. So the average = 1197/31 = \$38{19/31}\$. 