Averages Quiz Set 016

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Question 1

There is a sequence of 60 consecutive odd numbers. The average of first 18 of them is 78. What is the average of all the 60 numbers?

 A

120.

 B

121.

 C

119.

 D

118.

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 18 terms as 78. So a + 18 - 1 = 78, which gives a = 61. The average of first 60 terms would be a + 60 - 1 = 61 + 60 - 1 = 120.


Question 2

370 men and 555 women are employed in a farm. The average wage per person is Rs. 97. What is the wage of a man if women are paid Rs. 5 less?

 A

Rs. 100.

 B

Rs. 101.

 C

Rs. 99.

 D

Rs. 102.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average ${x × 370 + (x - 5) × 555}/{370 + 555}$ = 97. This equation can be solved for x to get Rs. 100 as the answer.


Question 3

A, B and C are three numbers. The average of A, B and C is 29. The average of A and B is 16, and the average of B and C is 69, what is the value of number B?

 A

83.

 B

84.

 C

82.

 D

81.

Soln.
Ans: a

By the given conditions, A + B = 2 × 16 = 32. Similarly, B + C = 2 × 69 = 138. Adding we get A + 2B + C = 170. We have also been given that A + B + C = 3 × 29 = 87. Subtracting, we get B = 170 - 87 = 83.


Question 4

If the average of p and q is 28, the average of q and r is 48, and of r and p is 72, then what is the value of p?

 A

52.

 B

53.

 C

51.

 D

54.

Soln.
Ans: a

We have three equations (p + q)/2 = average of pq, (q + r)/2 = average of qr and (r + p)/2 = average of rp. Adding these three we get p + q + r = (average of pq + average of qr + average of rp) = (28 + 48 + 72) = 148. So p = 148 - (q + r) = 148 - (2 × average of q and r) = 148 - 2 × 48 = 52.


Question 5

Two of the 32 numbers are 32 and 42, If these two are excluded the average of the remaining 30 numbers is 1 more than the average of all the 32 numbers. What is the average of all the 32 numbers?

 A

22.

 B

23.

 C

21.

 D

24.

Soln.
Ans: a

Let the required average be x. Then $32x - (32 + 42) = 30 × (x - 1).$ which gives $32x - 74 = 30 × (x - 1).$ Solving for x we get x = 22.


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This Blog Post/Article "Averages Quiz Set 016" 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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