# Averages Quiz Set 015

### Question 1

The average weight of 13 students of a class is 39 Kg, whereas the average weight of remaining 17 students is 30 Kg. What is the average weight of all 30 students?

A

\$33{9/10}\$.

B

\$35{2/29}\$.

C

\$32{25/31}\$.

D

\$36{9/28}\$.

Soln.
Ans: a

Total weight of 13 students is 13 × 39 = 507. Similarly, the total weight of remaining 17 students is 17 × 30 = 510. The total weight of all 30 students is 507 + 510 = 1017. So the average = 1017/30 = \$33{9/10}\$.

### Question 2

What is the increase in the average of 14 numbers if the number 12 is replaced by 152?

A

10.

B

11.

C

9.

D

12.

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 = 152, r = 12, n = 14. So increase = \$(152 - 12)/14\$ = 10.

### Question 3

There are three sections in school with 30, 30 and 40 students respectively. The average weight of a student in these sections, respectively, is 6, 2 and 6 Kg. What is the average weight of all the the students of the combined sections?

A

\$4{4/5}\$.

B

\$4{81/100}\$.

C

\$4{79/100}\$.

D

\$4{39/50}\$.

Soln.
Ans: a

The sums of the weights of all the students is 30 × 6 + 30 × 2 + 40 × 6 = 480. The required average = 480/total students = \$480/{30 + 30 + 40}\$ = \${24/5}\$, which is same as: \$4{4/5}\$.

### Question 4

Two of the 26 numbers are 22 and 50, If these two are excluded the average of the remaining 24 numbers is 1 more than the average of all the 26 numbers. What is the average of all the 26 numbers?

A

24.

B

25.

C

23.

D

26.

Soln.
Ans: a

Let the required average be x. Then \$26x - (22 + 50) = 24 × (x - 1).\$ which gives \$26x - 72 = 24 × (x - 1).\$ Solving for x we get x = 24.

### Question 5

The sales(in rupees) of a gift shop for six consecutive days is 1254, 5016, 4230, 876, 984 and 2076. What is the overall average sale for these six days?

A

Rs.2406.

B

Rs.2412.

C

Rs.2400.

D

Rs.2418.

Soln.
Ans: a

The total sale on first six days is 1254 + 5016 + 4230 + 876 + 984 + 2076 = 14436. The average for 6 days is: 14436/6, which gives Rs. 2406.