# Averages Quiz Set 020

### Question 1

The average age of three friends 3 years ago was 27 years. The average age of two them 5 years ago was 10 years. What is the present age of the third friend?

A

60 years.

B

61 years.

C

59 years.

D

58 years.

Soln.
Ans: a

Let the present ages of the three friends be a, b and c. We are given \${(b - 5) + (c - 5)}/2\$ = 10. Which gives b + c = 30. We are also given \${(a - 3) + (b - 3) + (c - 3)}/3\$ = 27, which gives a + b + c = 3 * 27 + 9 = 90. Putting b + c here we get a = 90 - (b + c) = 90 - 30 = 60 years.

### Question 2

In a cricket match of 50 overs a team has to chase a target of 326 runs. During the first 20 overs it has scored at the rate of 4.3 runs per over. What is the required run rate for the remaining 30 overs?

A

8.

B

9.

C

7.

D

6.

Soln.
Ans: a

The runs already scored = scoring rate × overs = \$4.3 × 20\$ = 86. Required number of runs = 326 - 86 = 240 in 50 - 20 = 30 overs. Required rate = 240/30 = 8.

### Question 3

If the average of p and q is 28, the average of q and r is 48, and of r and p is 72, then what is the value of p?

A

52.

B

53.

C

51.

D

54.

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) = (28 + 48 + 72) = 148. So p = 148 - (q + r) = 148 - (2 × average of q and r) = 148 - 2 × 48 = 52.

### Question 4

Average marks of class of 24 students is 52. What will be the average if each student is given 8 as grace marks?

A

60.

B

61.

C

59.

D

58.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula \$52 = x/24\$, which gives x = \$52 × 24 = 1248\$. When grace marks = 8 are added for each of the 24 students, the new total becomes \$1248 + 24 × 8 = 1440\$, the new average becomes \$1440/24 = 60\$. TIP: As a shortcut, the new average = old average + grace marks.

### Question 5

Two of the 28 numbers are 24 and 58, If these two are excluded the average of the remaining 26 numbers is 1 less than the average of all the 28 numbers. What is the average of all the 28 numbers?

A

28.

B

29.

C

27.

D

30.

Soln.
Ans: a

Let the required average be x. Then \$28x - (24 + 58) = 26 × (x - 1).\$ which gives \$28x - 82 = 26 × (x - 1).\$ Solving for x we get x = 28. 