Averages Quiz Set 017

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Question 1

A box contains 5 marbles each having a weight of 144 grams. The box also contains 25 marbles each having a weight of 114 grams. What is the average weight of all the marbles in the box?

 A

119 grams.

 B

120 grams.

 C

118 grams.

 D

117 grams.

Soln.
Ans: a

The weighted average = ${5 × 144 + 25 × 114}/30$, which equals ${720 + 2850}/30$ = 119.


Question 2

There is a sequence of 57 consecutive odd numbers. The average of first 13 of them is 203. What is the average of all the 57 numbers?

 A

247.

 B

248.

 C

246.

 D

245.

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 13 terms as 203. So a + 13 - 1 = 203, which gives a = 191. The average of first 57 terms would be a + 57 - 1 = 191 + 57 - 1 = 247.


Question 3

The average weight of 16 students of a class is 31 Kg, whereas the average weight of remaining 16 students is 28 Kg. What is the average weight of all 32 students?

 A

$29{1/2}$.

 B

$30{14/31}$.

 C

$28{20/33}$.

 D

$31{7/15}$.

Soln.
Ans: a

Total weight of 16 students is 16 × 31 = 496. Similarly, the total weight of remaining 16 students is 16 × 28 = 448. The total weight of all 32 students is 496 + 448 = 944. So the average = 944/32 = $29{1/2}$.


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

Two of the 22 numbers are 30 and 54, If these two are excluded the average of the remaining 20 numbers is 1 more than the average of all the 22 numbers. What is the average of all the 22 numbers?

 A

32.

 B

33.

 C

31.

 D

34.

Soln.
Ans: a

Let the required average be x. Then $22x - (30 + 54) = 20 × (x - 1).$ which gives $22x - 84 = 20 × (x - 1).$ Solving for x we get x = 32.


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This Blog Post/Article "Averages Quiz Set 017" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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