# Averages Quiz Set 016

### 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.