# Averages Quiz Set 019

### Question 1

A, B and C are three numbers. The average of A, B and C is 25. The average of A and B is 14, and the average of B and C is 49, what is the value of number B?

A

51.

B

52.

C

50.

D

49.

Soln.
Ans: a

By the given conditions, A + B = 2 × 14 = 28. Similarly, B + C = 2 × 49 = 98. Adding we get A + 2B + C = 126. We have also been given that A + B + C = 3 × 25 = 75. Subtracting, we get B = 126 - 75 = 51.

### Question 2

In a cricket match of 50 overs a team has to chase a target of 425 runs. During the first 10 overs it has scored at the rate of 2.5 runs per over. What is the required run rate for the remaining 40 overs?

A

10.

B

11.

C

9.

D

8.

Soln.
Ans: a

The runs already scored = scoring rate × overs = \$2.5 × 10\$ = 25. Required number of runs = 425 - 25 = 400 in 50 - 10 = 40 overs. Required rate = 400/40 = 10.

### Question 3

In a cricket match of 50 overs a team has to chase a target of 594 runs. During the first 10 overs it has scored at the rate of 3.4 runs per over. What is the required run rate for the remaining 40 overs?

A

14.

B

15.

C

13.

D

12.

Soln.
Ans: a

The runs already scored = scoring rate × overs = \$3.4 × 10\$ = 34. Required number of runs = 594 - 34 = 560 in 50 - 10 = 40 overs. Required rate = 560/40 = 14.

### Question 4

Each of the 9 athletes of a Olympics has a timings 88 seconds. If a new athlete with a timings 45 seconds more than the average of all 10 athletes is added, what is the sum total of the values of all 10 athletes?

A

930 seconds.

B

931 seconds.

C

929 seconds.

D

928 seconds.

Soln.
Ans: a

Let the average of all 10 athletes be x, then the required total is T = 10x. By averages, \$x = {9 × 88 + (x + 45)}/10\$ which is same as \$x × 10 = {9 × 88 + (x + 45)}\$, which is same as \$T = {9 × 88 + (T/10 + 45)}\$, solving for T we get 930 seconds.

### Question 5

Two of the 36 numbers are 28 and 58, If these two are excluded the average of the remaining 34 numbers is 1 less than the average of all the 36 numbers. What is the average of all the 36 numbers?

A

26.

B

27.

C

25.

D

28.

Soln.
Ans: a

Let the required average be x. Then \$36x - (28 + 58) = 34 × (x - 1).\$ which gives \$36x - 86 = 34 × (x - 1).\$ Solving for x we get x = 26. 