# Averages Quiz Set 017

### Question 1

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.

### Question 2

There is a sequence of 57 consecutive odd numbers. The average of first 13 of them is 203. What is the average of all the 57 numbers?

A

247.

B

248.

C

246.

D

245.

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 13 terms as 203. So a + 13 - 1 = 203, which gives a = 191. The average of first 57 terms would be a + 57 - 1 = 191 + 57 - 1 = 247.

### Question 3

The average weight of 16 students of a class is 31 Kg, whereas the average weight of remaining 16 students is 28 Kg. What is the average weight of all 32 students?

A

\$29{1/2}\$.

B

\$30{14/31}\$.

C

\$28{20/33}\$.

D

\$31{7/15}\$.

Soln.
Ans: a

Total weight of 16 students is 16 × 31 = 496. Similarly, the total weight of remaining 16 students is 16 × 28 = 448. The total weight of all 32 students is 496 + 448 = 944. So the average = 944/32 = \$29{1/2}\$.

### Question 4

Average weight of a group of 30 boys is 34 Kg. Later it was found that the weighing machine was showing 2 Kg more than the actual weight. What is the actual average weight?

A

32.

B

33.

C

31.

D

30.

Soln.
Ans: a

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula \$34 = x/30\$, which gives x = \$34 × 30 = 1020\$. When weight of each of the 30 boys is reduced by 2 Kg, the new total becomes \$1020 - 30 × 2 = 960\$, the new average becomes \$960/30 = 32\$. TIP: As a shortcut, the new average = old average - error in weighing machine.

### Question 5

Two of the 22 numbers are 30 and 54, If these two are excluded the average of the remaining 20 numbers is 1 more than the average of all the 22 numbers. What is the average of all the 22 numbers?

A

32.

B

33.

C

31.

D

34.

Soln.
Ans: a

Let the required average be x. Then \$22x - (30 + 54) = 20 × (x - 1).\$ which gives \$22x - 84 = 20 × (x - 1).\$ Solving for x we get x = 32.