# Averages Quiz Set 018

### Question 1

A, B and C are three numbers. The average of A, B and C is 30. The average of A and B is 17, and the average of B and C is 78, what is the value of number B?

A

100.

B

101.

C

99.

D

98.

Soln.
Ans: a

By the given conditions, A + B = 2 × 17 = 34. Similarly, B + C = 2 × 78 = 156. Adding we get A + 2B + C = 190. We have also been given that A + B + C = 3 × 30 = 90. Subtracting, we get B = 190 - 90 = 100.

### Question 2

The cost per unit of a commodity in three successive years is Rs.10/unit, Rs.14/unit and Rs.16/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

\$12{108/131}\$.

B

\$13{1/3}\$.

C

10.

D

8.

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 = 10, r2 = 14, r3 = 16, we get \$12{108/131}\$. 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 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

What is the increase in the average of 17 numbers if the number 11 is replaced by 232?

A

13.

B

14.

C

12.

D

15.

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 = 232, r = 11, n = 17. So increase = \$(232 - 11)/17\$ = 13.

### Question 5

There is a sequence of 66 consecutive odd numbers. The average of first 26 of them is 82. What is the average of all the 66 numbers?

A

122.

B

123.

C

121.

D

120.

Soln.
Ans: a

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is \${a + (a + (n-1) × 2)}/2\$ which is = a + n-1. We are given the average of first 26 terms as 82. So a + 26 - 1 = 82, which gives a = 57. The average of first 66 terms would be a + 66 - 1 = 57 + 66 - 1 = 122.