# Averages Quiz Set 014

### Question 1

What is the increase in the average of 11 numbers if the number 13 is replaced by 112?

A

9.

B

10.

C

8.

D

11.

Soln.
Ans: a

If a number r is replaced by a number R, the increase/decrease of average is determined according to the formula \$(R - r)/n\$. So in our case we have R = 112, r = 13, n = 11. So increase = \$(112 - 13)/11\$ = 9.

### Question 2

There are three sections in school with 30, 40 and 40 students respectively. The average weight of a student in these sections, respectively, is 6, 3 and 4 Kg. What is the average weight of all the the students of the combined sections?

A

\$4{2/11}\$.

B

\$4{21/110}\$.

C

\$4{19/110}\$.

D

\$4{9/55}\$.

Soln.
Ans: a

The sums of the weights of all the students is 30 × 6 + 40 × 3 + 40 × 4 = 460. The required average = 460/total students = \$460/{30 + 40 + 40}\$ = \${46/11}\$, which is same as: \$4{2/11}\$.

### Question 3

What is the increase in the average of 14 numbers if the number 12 is replaced by 152?

A

10.

B

11.

C

9.

D

12.

Soln.
Ans: a

If a number r is replaced by a number R, the increase/decrease of average is determined according to the formula \$(R - r)/n\$. So in our case we have R = 152, r = 12, n = 14. So increase = \$(152 - 12)/14\$ = 10.

### Question 4

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 5

The sales(in rupees) of a gift shop for six consecutive days is 5028, 3042, 4446, 786, 5376 and 2838. What is the overall average sale for these six days?

A

Rs.3586.

B

Rs.3592.

C

Rs.3580.

D

Rs.3598.

Soln.
Ans: a

The total sale on first six days is 5028 + 3042 + 4446 + 786 + 5376 + 2838 = 21516. The average for 6 days is: 21516/6, which gives Rs. 3586. 