# Averages Quiz Set 011

### Question 1

There are three sections in school with 30, 30 and 40 students respectively. The average weight of a student in these sections, respectively, is 6, 2 and 6 Kg. What is the average weight of all the the students of the combined sections?

A

\$4{4/5}\$.

B

\$4{81/100}\$.

C

\$4{79/100}\$.

D

\$4{39/50}\$.

Soln.
Ans: a

The sums of the weights of all the students is 30 × 6 + 30 × 2 + 40 × 6 = 480. The required average = 480/total students = \$480/{30 + 30 + 40}\$ = \${24/5}\$, which is same as: \$4{4/5}\$.

### Question 2

There is a sequence of 66 consecutive odd numbers. The average of first 26 of them is 82. What is the average of all the 66 numbers?

A

122.

B

123.

C

121.

D

120.

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 26 terms as 82. So a + 26 - 1 = 82, which gives a = 57. The average of first 66 terms would be a + 66 - 1 = 57 + 66 - 1 = 122.

### Question 3

Average marks of class of 20 students is 85. What will be the average if each student is given 6 as grace marks?

A

91.

B

92.

C

90.

D

89.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula \$85 = x/20\$, which gives x = \$85 × 20 = 1700\$. When grace marks = 6 are added for each of the 20 students, the new total becomes \$1700 + 20 × 6 = 1820\$, the new average becomes \$1820/20 = 91\$. TIP: As a shortcut, the new average = old average + grace marks.

### Question 4

If the average of p and q is 20, the average of q and r is 54, and of r and p is 64, then what is the value of p?

A

30.

B

31.

C

29.

D

32.

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) = (20 + 54 + 64) = 138. So p = 138 - (q + r) = 138 - (2 × average of q and r) = 138 - 2 × 54 = 30.

### Question 5

The average weight of the 9 bogies of a train increases by 4 Kg when a new bogie replaces a bogie of weight 2 Kg. What is the weight of the new bogie.

A

38.

B

39.

C

37.

D

40.

Soln.
Ans: a

The total increase of weight = 9 × 4 = 36. So the weight of the new bogie = 2 + 36 = 38 Kg. 