# Averages Quiz Set 003

### Question 1

The average weight of the 11 bogies of a train increases by 14 Kg when a new bogie replaces a bogie of weight 13 Kg. What is the weight of the new bogie.

A

167.

B

168.

C

166.

D

169.

Soln.
Ans: a

The total increase of weight = 11 × 14 = 154. So the weight of the new bogie = 13 + 154 = 167 Kg.

### Question 2

412 men and 103 women are employed in a farm. The average wage per person is Rs. 194. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 195.

B

Rs. 196.

C

Rs. 194.

D

Rs. 197.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 412 + (x - 5) × 103}/{412 + 103}\$ = 194. This equation can be solved for x to get Rs. 195 as the answer.

### Question 3

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 4

A, B and C are three numbers. The average of A, B and C is 26. The average of A and B is 14, and the average of B and C is 37, what is the value of number B?

A

24.

B

25.

C

23.

D

22.

Soln.
Ans: a

By the given conditions, A + B = 2 × 14 = 28. Similarly, B + C = 2 × 37 = 74. Adding we get A + 2B + C = 102. We have also been given that A + B + C = 3 × 26 = 78. Subtracting, we get B = 102 - 78 = 24.

### Question 5

The average weight of 17 students of a class is 27 Kg, whereas the average weight of remaining 16 students is 33 Kg. What is the average weight of all 33 students?

A

\$29{10/11}\$.

B

\$30{27/32}\$.

C

\$29{1/34}\$.

D

\$31{26/31}\$.

Soln.
Ans: a

Total weight of 17 students is 17 × 27 = 459. Similarly, the total weight of remaining 16 students is 16 × 33 = 528. The total weight of all 33 students is 459 + 528 = 987. So the average = 987/33 = \$29{10/11}\$. 