# Averages Quiz Set 010

### Question 1

A box contains 5 marbles each having a weight of 108 grams. The box also contains 25 marbles each having a weight of 72 grams. What is the average weight of all the marbles in the box?

A

78 grams.

B

79 grams.

C

77 grams.

D

76 grams.

Soln.
Ans: a

The weighted average = \${5 × 108 + 25 × 72}/30\$, which equals \${540 + 1800}/30\$ = 78.

### Question 2

Each of the 8 girls of a class has a score 28 marks. If a new girl with a score 56 marks more than the average of all 9 girls is added, what is the sum total of the values of all 9 girls?

A

315 marks.

B

316 marks.

C

314 marks.

D

313 marks.

Soln.
Ans: a

Let the average of all 9 girls be x, then the required total is T = 9x. By averages, \$x = {8 × 28 + (x + 56)}/9\$ which is same as \$x × 9 = {8 × 28 + (x + 56)}\$, which is same as \$T = {8 × 28 + (T/9 + 56)}\$, solving for T we get 315 marks.

### Question 3

The average weight of the 17 bogies of a train increases by 13 Kg when a new bogie replaces a bogie of weight 9 Kg. What is the weight of the new bogie.

A

230.

B

231.

C

229.

D

232.

Soln.
Ans: a

The total increase of weight = 17 × 13 = 221. So the weight of the new bogie = 9 + 221 = 230 Kg.

### Question 4

387 men and 258 women are employed in a farm. The average wage per person is Rs. 128. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 130.

B

Rs. 131.

C

Rs. 129.

D

Rs. 132.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 387 + (x - 5) × 258}/{387 + 258}\$ = 128. This equation can be solved for x to get Rs. 130 as the answer.

### Question 5

The average weight of 16 students of a class is 31 Kg, whereas the average weight of remaining 16 students is 28 Kg. What is the average weight of all 32 students?

A

\$29{1/2}\$.

B

\$30{14/31}\$.

C

\$28{20/33}\$.

D

\$31{7/15}\$.

Soln.
Ans: a

Total weight of 16 students is 16 × 31 = 496. Similarly, the total weight of remaining 16 students is 16 × 28 = 448. The total weight of all 32 students is 496 + 448 = 944. So the average = 944/32 = \$29{1/2}\$. 