# Averages Quiz Set 004

### Question 1

The sales(in rupees) of a karyana store for five consecutive days is 2262, 666, 1740, 3216, 4926. What should be the sale on the sixth day so that the overall average sale is 2281?

A

Rs.876.

B

Rs.882.

C

Rs.870.

D

Rs.888.

Soln.
Ans: a

The total sale on first five days is 2262 + 666 + 1740 + 3216 + 4926 = 12810. Let the sale on 6th day be x. The average for 6 days is: 2281 = \${12810 + x}/6\$ which gives x = \$6 × 2281 - 12810\$ = Rs. 876.

### 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

What is the increase in the average of 10 numbers if the number 5 is replaced by 85?

A

8.

B

9.

C

7.

D

10.

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 = 85, r = 5, n = 10. So increase = \$(85 - 5)/10\$ = 8.

### Question 4

What is the average of first 343 natural numbers?

A

172.

B

173.

C

171.

D

170.

Soln.
Ans: a

The sum of first n natural numbers is \$(n × (n + 1))/2\$. The average is \${(n × (n + 1))/2}/n\$ which is \$(n + 1)/2.\$ Putting n = 343, we get average = 172.

### Question 5

Average weight of a group of 44 boys is 28 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

26.

B

27.

C

25.

D

24.

Soln.
Ans: a

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula \$28 = x/44\$, which gives x = \$28 × 44 = 1232\$. When weight of each of the 44 boys is reduced by 2 Kg, the new total becomes \$1232 - 44 × 2 = 1144\$, the new average becomes \$1144/44 = 26\$. TIP: As a shortcut, the new average = old average - error in weighing machine. 