__Practice Problems on Averages Set – 4__**1. There are 45 students in a class. The no. of boys is 5 more than girls. The average weight of boys is 5 more than average weight of girls. The total weight of boys is 100 more than girls. Calculate the average weight of the class?**

(a) 50.1kg

(b) 51.1 kg

(c) 49.1kg

(d) 50kg

(e)52kg

**Answer:**B)

**Explanation:**Total student =45

Let no of boys be x then girls will be 45-x.

As given x = 45-x +5.

Then x = 25.

Let total weight of boys and girls be A and B
respectively.

Then A/25 + 5 = B/20, also A = 100 + B.

**2. If there are 10 people in a trip then the average height of all is 160 cm, but if 8 people go in the trip then the average height reduces by 1 cm. find the average height of remaining two?**

(a) 160 cm

(b) 164 cm

(c) 155 cm

(d) 170 cm

(e) 164.5 cm

**Answer:**

**B)**

**Explanation:**Total height of 10 people is 1600 cm (10*160)

When people = 8, total height is 1272 cm
(8*159)

Average of remaining two is (1600-1272)/ 2 =
164 cm.

**3. In a family of 8 of three generation, there are two fathers, two mothers, two brothers, and two male children. The total age of the female member of the family is 5 less than total age of male member of the family. What is the difference in the average age of male and female member of the family?**

(a) 5

(b) 10

(c) 15

(d) 12

(e) Data inadequate

**Answer:**

**E)**

**Explanation:**Female are 3 and male are 5

Total age of male – total age of female = 5.

No other information is given so data
inadequate

**4. The average of three numbers is 59. When six more numbers are included the average becomes one-third more of the previous average, what is difference between the averages of the two set of numbers?**

(a) 19.4

(b) 19.3

(c) 19.5

(d) 9.7

(e) 20.17

**Answer:**

**E)**

**Explanation:**a+b+c= (3*59)

Let six new numbers be y then

a+b+c+y= (59 +1/3) * 9

On solving we get difference as 20.17

**5. Two trains moving in opposite direction have an average speed of 56km/hr both. If both runs in same direction than the average speed of both train will be?**

(a) 56km/hr

(b) 50 km/hr

(c) 56.7 km/hr

(d) cannot be determined

(e) None

**Answer:**

**D)**

**Explanation:**Let speed of both the train be x and y, then 2xy/(x+y) = 56 km/hr.

If both run in same direction than average
speed will be 2xy/(x-y).

Since there is no data for x and y so answer
is (d).

**6. There are 35 students in a lecture of physics, in which the difference between the girls and boys is 5. The average of marks got by girls is 5 more than boys and the total marks got by boys are 50 less than girls. What is the average mark of total students?**

(a) 160/7

(b) 150/9

(c) 130/9

(d) 190/9

(e)190/7

**Answer:**

**E)**

**Explanation:**Case 1: when boys> girls

Total student =35

Let no of boys be x then girls will be 35-x.

As given x = 35-x +5.

Then x = 20. Let total weight of boys and
girls be A and B respectively.

Then A/15 + 5 = B/20, also A = 50 + B.

On solving we get a negative value which is
incorrect, so this assumption is wrong.

Case 2: when boys< girls

Total student =35

Let no of girls be x then boys will be 35-x.

As given x = 35-x +5.

Then x = 20. Let total weight of boys and
girls be A and B respectively.

Then A/20 - 5 = B/15, also B = 50 + A.

On solving we get average marks as 190/9

**7. Four boxes full of apples are placed one by one in a big box. The average height and length of the small boxes are in ratio of 5:7. The average of breadth of all boxes is 4 more than average of height. Calculate the approximate average volume of all four boxes if total height of all boxes is 60 cm.**

(a) 48857

(b) 48867

(c) 47885

(d) 48897

(e) None of these

**Answer:**

**A)**

**Explanation:**The ratio between height and length is 5:7 and also average breath is 4 more than average height. Total height is 60 cm.

Then we get total breath as 19*4=68 then total
length will be 300/7.

Then average volume (total L* total B * total
H) will be total volume/4. i.e. 48857.

**8. The average age of Arun and his wife was 25 at the time of their marriage and it increases by 3 at the birth of their child. What is the average age of the three at present at the 5th birthday of their son?**

(a) 53/3

(b) 65/3

(c) 71/3

(d) 25

(e)23

**Answer:**

**C)**

**Explanation:**Arun +wife = 50

Arun + wife = 56 at the birth of their son.

After 5 years average age =71/3

**9. The difference between the averages of two set of numbers is 6, if total numbers are 10 and the total sum of second set is 56. What is the average of sum of both set?**

(a) 50

(b) 65

(c) 60

(d) cannot be determined

(e) None of these

**Answer:**

**D)**

**Explanation:**Let the two set sum be A and B and total numbers in each set be n and m respectively.

A/n –B/m =6

Also m+n =10, B=56

On solving inadequate data problem take place
so answer is (d).

**10. The average score of a cricketer is 100 in 15 matches, if his average score for 7 matches is 10 more than average score of 8 matches than what is difference in the averages of first 7 matches and last 8 matches if the cricketer scores 480 runs in last 8 matches?**

(a) 5

(b) 4

(c) 6

(d) 12

(e) 10

**Answer:**

**E)**

**Explanation:**Total score = 1500 runs.

Also total runs in 7 matches/7 = 10 + total
runs in last 8 matches/8

Total runs in 8 matches are 480. On solving we
get average of 7 matches as 70,

Difference is 10.