# Averages Quiz Set 015

### Question 1

A, B and C are three numbers. The average of A, B and C is 30. The average of A and B is 17, and the average of B and C is 78, what is the value of number B?

A

100.

B

101.

C

99.

D

98.

Soln.
Ans: a

By the given conditions, A + B = 2 × 17 = 34. Similarly, B + C = 2 × 78 = 156. Adding we get A + 2B + C = 190. We have also been given that A + B + C = 3 × 30 = 90. Subtracting, we get B = 190 - 90 = 100.

### Question 2

What is the average of first 383 natural numbers?

A

192.

B

193.

C

191.

D

190.

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 = 383, we get average = 192.

### Question 3

Two of the 22 numbers are 30 and 54, If these two are excluded the average of the remaining 20 numbers is 1 less 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.

### Question 4

What is the average of first 527 natural numbers?

A

264.

B

265.

C

263.

D

262.

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 = 527, we get average = 264.

### Question 5

The sales(in rupees) of a gift shop for six consecutive days is 3318, 3690, 2466, 5346, 1692 and 1470. What is the overall average sale for these six days?

A

Rs.2997.

B

Rs.3003.

C

Rs.2991.

D

Rs.3009.

Soln.
Ans: a

The total sale on first six days is 3318 + 3690 + 2466 + 5346 + 1692 + 1470 = 17982. The average for 6 days is: 17982/6, which gives Rs. 2997. 