# Averages Quiz Set 003

### Question 1

If the average of p and q is 24, the average of q and r is 52, and of r and p is 60, then what is the value of p?

A

32.

B

33.

C

31.

D

34.

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) = (24 + 52 + 60) = 136. So p = 136 - (q + r) = 136 - (2 × average of q and r) = 136 - 2 × 52 = 32.

### Question 2

The average age of three friends 3 years ago was 30 years. The average age of two them 5 years ago was 13 years. What is the present age of the third friend?

A

63 years.

B

64 years.

C

62 years.

D

61 years.

Soln.
Ans: a

Let the present ages of the three friends be a, b and c. We are given \${(b - 5) + (c - 5)}/2\$ = 13. Which gives b + c = 36. We are also given \${(a - 3) + (b - 3) + (c - 3)}/3\$ = 30, which gives a + b + c = 3 * 30 + 9 = 99. Putting b + c here we get a = 99 - (b + c) = 99 - 36 = 63 years.

### Question 3

There is a sequence of 64 consecutive odd numbers. The average of first 29 of them is 137. What is the average of all the 64 numbers?

A

172.

B

173.

C

171.

D

170.

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 29 terms as 137. So a + 29 - 1 = 137, which gives a = 109. The average of first 64 terms would be a + 64 - 1 = 109 + 64 - 1 = 172.

### Question 4

There are three sections in school with 20, 40 and 30 students respectively. The average weight of a student in these sections, respectively, is 2, 5 and 2 Kg. What is the average weight of all the the students of the combined sections?

A

\$3{1/3}\$.

B

\$3{31/90}\$.

C

\$3{29/90}\$.

D

\$3{14/45}\$.

Soln.
Ans: a

The sums of the weights of all the students is 20 × 2 + 40 × 5 + 30 × 2 = 300. The required average = 300/total students = \$300/{20 + 40 + 30}\$ = \${10/3}\$, which is same as: \$3{1/3}\$.

### Question 5

Average weight of a group of 41 boys is 75 Kg. Later it was found that the weighing machine was showing 4 Kg more than the actual weight. What is the actual average weight?

A

71.

B

72.

C

70.

D

69.

Soln.
Ans: a

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula \$75 = x/41\$, which gives x = \$75 × 41 = 3075\$. When weight of each of the 41 boys is reduced by 4 Kg, the new total becomes \$3075 - 41 × 4 = 2911\$, the new average becomes \$2911/41 = 71\$. TIP: As a shortcut, the new average = old average - error in weighing machine.