# Averages Quiz Set 006

### Question 1

What is the average of first 527 natural numbers?

A

264.

B

265.

C

263.

D

262.

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 = 527, we get average = 264.

### Question 2

A box contains 5 marbles each having a weight of 144 grams. The box also contains 25 marbles each having a weight of 96 grams. What is the average weight of all the marbles in the box?

A

104 grams.

B

105 grams.

C

103 grams.

D

102 grams.

Soln.
Ans: a

The weighted average = \${5 × 144 + 25 × 96}/30\$, which equals \${720 + 2400}/30\$ = 104.

### Question 3

The cost per unit of a commodity in three successive years is Rs.12/unit, Rs.6/unit and Rs.2/unit. If the annual spending of a family remains fixed, what is the average cost per unit for all the three combined years together?

A

4.

B

\$6{2/3}\$.

C

5.

D

4.

Soln.
Ans: a

Let the annual spending be Rs. M. The catch in this question is that the spending remains fixed, so the consumption varies from year to year. We shall calculate the total consumption first. Let r1, r2 and r3 be the rates for the three successive years. Consumption in first year = M/r1. Similarly, we get M/r2 and M/r3. So total consumption is \$M/{r1} + M/{r2} + M/{r3}\$. Money spent in three years is 3M. So the required average = \${3M}/{M/{r1} + M/{r2} + M/{r3}}\$ which simplifies to \${3r1r2r3}/{r1r2 + r2r3 + r3r1}\$. Putting r1 = 12, r2 = 6, r3 = 2, we get 4. You might be wondering why I derived the formula first. The reason is that sometimes it is better to postpone calculations till the end.

### Question 4

What is the average of first 343 natural numbers?

A

172.

B

173.

C

171.

D

170.

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 = 343, we get average = 172.

### 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}\$.

Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer