# Averages Quiz Set 012

### Question 1

The cost per unit of a commodity in three successive years is Rs.14/unit, Rs.8/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

\$11{17/29}\$.

B

\$12{2/3}\$.

C

\$9{1/2}\$.

D

\$7{3/5}\$.

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 = 14, r2 = 8, r3 = 16, we get \$11{17/29}\$. 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 2

The average weight of the 17 bogies of a train increases by 3 Kg when a new bogie replaces a bogie of weight 11 Kg. What is the weight of the new bogie.

A

62.

B

63.

C

61.

D

64.

Soln.
Ans: a

The total increase of weight = 17 × 3 = 51. So the weight of the new bogie = 11 + 51 = 62 Kg.

### Question 3

Two of the 26 numbers are 22 and 50, If these two are excluded the average of the remaining 24 numbers is 1 less than the average of all the 26 numbers. What is the average of all the 26 numbers?

A

24.

B

25.

C

23.

D

26.

Soln.
Ans: a

Let the required average be x. Then \$26x - (22 + 50) = 24 × (x - 1).\$ which gives \$26x - 72 = 24 × (x - 1).\$ Solving for x we get x = 24.

### Question 4

Average weight of a group of 30 boys is 34 Kg. Later it was found that the weighing machine was showing 2 Kg more than the actual weight. What is the actual average weight?

A

32.

B

33.

C

31.

D

30.

Soln.
Ans: a

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula \$34 = x/30\$, which gives x = \$34 × 30 = 1020\$. When weight of each of the 30 boys is reduced by 2 Kg, the new total becomes \$1020 - 30 × 2 = 960\$, the new average becomes \$960/30 = 32\$. TIP: As a shortcut, the new average = old average - error in weighing machine.

### Question 5

154 men and 616 women are employed in a farm. The average wage per person is Rs. 141. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 145.

B

Rs. 146.

C

Rs. 144.

D

Rs. 147.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 154 + (x - 5) × 616}/{154 + 616}\$ = 141. This equation can be solved for x to get Rs. 145 as the answer.