Averages Quiz Set 002

Question 1

The average age of three friends 3 years ago was 31 years. The average age of two them 5 years ago was 12 years. What is the present age of the third friend?

A

68 years.

B

69 years.

C

67 years.

D

66 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\$ = 12. Which gives b + c = 34. We are also given \${(a - 3) + (b - 3) + (c - 3)}/3\$ = 31, which gives a + b + c = 3 * 31 + 9 = 102. Putting b + c here we get a = 102 - (b + c) = 102 - 34 = 68 years.

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

Average marks of class of 10 students is 62. What will be the average if each student is given 8 as grace marks?

A

70.

B

71.

C

69.

D

68.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula \$62 = x/10\$, which gives x = \$62 × 10 = 620\$. When grace marks = 8 are added for each of the 10 students, the new total becomes \$620 + 10 × 8 = 700\$, the new average becomes \$700/10 = 70\$. TIP: As a shortcut, the new average = old average + grace marks.

Question 4

412 men and 103 women are employed in a farm. The average wage per person is Rs. 194. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 195.

B

Rs. 196.

C

Rs. 194.

D

Rs. 197.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 412 + (x - 5) × 103}/{412 + 103}\$ = 194. This equation can be solved for x to get Rs. 195 as the answer.

Question 5

154 men and 616 women are employed in a farm. The average wage per person is Rs. 141. What is the wage of a man if women are paid Rs. 5 less?

A

Rs. 145.

B

Rs. 146.

C

Rs. 144.

D

Rs. 147.

Soln.
Ans: a

Let the wage of a man and a woman be x and x - 5. We are given the average \${x × 154 + (x - 5) × 616}/{154 + 616}\$ = 141. This equation can be solved for x to get Rs. 145 as the answer.