# Averages Quiz Set 017

### Question 1

If the average of p and q is 38, the average of q and r is 56, and of r and p is 72, then what is the value of p?

A

54.

B

55.

C

53.

D

56.

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) = (38 + 56 + 72) = 166. So p = 166 - (q + r) = 166 - (2 × average of q and r) = 166 - 2 × 56 = 54.

### Question 2

Each of the 5 items of a sample has a value 78 units. If a new item with a value 55 units more than the average of all 6 items is added, what is the sum total of the values of all 6 items?

A

534 units.

B

535 units.

C

533 units.

D

532 units.

Soln.
Ans: a

Let the average of all 6 items be x, then the required total is T = 6x. By averages, \$x = {5 × 78 + (x + 55)}/6\$ which is same as \$x × 6 = {5 × 78 + (x + 55)}\$, which is same as \$T = {5 × 78 + (T/6 + 55)}\$, solving for T we get 534 units.

### Question 3

What is the increase in the average of 16 numbers if the number 2 is replaced by 34?

A

2.

B

3.

C

1.

D

4.

Soln.
Ans: a

If a number r is replaced by a number R, the increase/decrease of average is determined according to the formula \$(R - r)/n\$. So in our case we have R = 34, r = 2, n = 16. So increase = \$(34 - 2)/16\$ = 2.

### Question 4

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 5

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.