# Averages Quiz Set 019

### Question 1

There are three sections in school with 40, 40 and 40 students respectively. The average weight of a student in these sections, respectively, is 3, 3 and 2 Kg. What is the average weight of all the the students of the combined sections?

A

\$2{2/3}\$.

B

\$2{27/40}\$.

C

\$2{79/120}\$.

D

\$2{13/20}\$.

Soln.
Ans: a

The sums of the weights of all the students is 40 × 3 + 40 × 3 + 40 × 2 = 320. The required average = 320/total students = \$320/{40 + 40 + 40}\$ = \${8/3}\$, which is same as: \$2{2/3}\$.

### Question 2

The average number of visitors at a zoo on a Monday is 156, whereas it is 162 on other days of the week. What will be the average number of visitors in a 30-day month that begins on a Monday?

A

161.

B

162.

C

160.

D

159.

Soln.
Ans: a

The month begins on a Monday, so there will be 5 Mondays. The average = \${5 × 156 + 25 × 162}/30\$, which equals \${780 + 4050}/30\$ = 161.

### Question 3

Average marks of class of 28 students is 51. What will be the average if each student is given 7 as grace marks?

A

58.

B

59.

C

57.

D

56.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula \$51 = x/28\$, which gives x = \$51 × 28 = 1428\$. When grace marks = 7 are added for each of the 28 students, the new total becomes \$1428 + 28 × 7 = 1624\$, the new average becomes \$1624/28 = 58\$. TIP: As a shortcut, the new average = old average + grace marks.

### Question 4

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 5

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.