## Average Questions and Answers Part-4

1. 3 years ago the average of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:
a) 1 years
b) $$\frac{3}{2}$$ years
c) 2 years
d) 3 years

Explanation: Let age of the baby is x.
3 years ago total age of the family = 5 × 17 = 85 years
Total age of the 5 member at present time = 85 + 3*5 = 100 years
Total age of the family at present time including baby = 100 + X
The average of the family including baby at present time = 17 years
$$\frac{{100 + {\text{x}}}}{6} = 17$$
100 + X = 102
X = 102 - 100 = 2 years

2. The average salary of all the workers in a workshop is Rs. 8,000. The average salary of 7 technicians is Rs. 12,000 and the average salary of the rest is Rs. 6,000. The total number of workers in the workshop is:
a) 20
b) 21
c) 22
d) 23

Explanation: Let the rest workers = x
(7 + x) × 8000 = 12000 × 7 + 6000x
56000 + 8000x = 84000 + 6000x
2000x = 28000
x = 14
Total number of worker = 14 + 7 = 21

3. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
a) 6.25
b) 6.5
c) 6.75
d) 7

Explanation:
\eqalign{ & {\text{Required run rate}} \cr & = {\frac{{282 - \left( {3.2 \times 10} \right)}}{{40}}} \cr & = \frac{{250}}{{40}} \cr & = 6.25 \cr}

4. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
a) $$28\frac{4}{7}$$ years
b) $$31\frac{5}{7}$$ years
c) $$32\frac{1}{7}$$ years
d) None of these

Explanation:
\eqalign{ & {\text{Required average}} \cr & {\text{ = }} {\frac{{67 \times 2 + 35 \times 2 + 6 \times 3}}{{2 + 2 + 3}}} \cr & = {\frac{{134 + 70 + 18}}{7}} \cr & = \frac{{222}}{7} \cr & = 31\frac{5}{7}{\text{years}} \cr}

5. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
a) Rs. 4991
b) Rs. 5991
c) Rs. 6001
d) Rs. 6991

Explanation: Total sale for 5 months
= Rs. (6435 + 6927 + 6855 + 7230 + 6562)
= Rs. 34009
Required sale = Rs. [(6500 × 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991

6. Mr. Joe’s family consists of six people-himself, his wife and their four children. It is known that the average age of the family immediately after the birth of the first, second, third and fourth child was 16, 15, 16 and 15 years respectively. Find the age of Mr. Joe’s eldest son if the present average age of the entire family is 16 years
a) 8 years
b) 12 years
c) 15 years
d) 16 years

Explanation: When the first child was born, the total age of all the family members = (16 × 3) years
= 48 years
When the second child was born, the total age of all the family members = (15 × 4) years
= 60 years
By the time the second child was born, each one of the 3 family members had grown by
\eqalign{ & = \left( {\frac{{60 - 48}}{3}} \right) \cr & = \frac{{12}}{3} \cr}
= 4 years
Hence, the age of eldest son when the second child was born = 4 years
When the third child was born, the total age of all the family members = (16 × 5) years
= 80 years
By the time, the third child was born, each one of the four family members had grown by
= $$\left( {\frac{{80 - 60}}{4}} \right)$$
= 5 years
The age of the eldest son when the third child was born = (4 + 5) years
= 9 years
When the fourth child was born, the total age of all the family members = (15 × 6) years
= 90 years
By the time, the fourth child was born, each of the five family members had grown by
= $$\left( {\frac{{90 - 80}}{5}} \right)$$
= 2 years
So, the age of the eldest son when the fourth child was born = (9 + 2) years
= 11 years
At present, the total age of all the 6 family members = (16 × 6) years
= 96 years
By now, each one of the 6 members have grown by
= $$\left( {\frac{{96 - 90}}{6}} \right)$$  years
= 1 year
The present age of the eldest son
= (11 + 1) years
= 12 years

7. Out of 10 teachers of a school, on teacher retires and in place of him a new teacher 25 years old joins. As a result of it average age of the teachers reduces by 3 years. Age of the retired teacher ( in years) is :
a) 55
b) 60
c) 58
d) 56

Explanation: Total number of teachers = 10
Age of new teacher = 25 years
Age of the retire teacher
= (25 + 3 × 10) years
= 55 years

8. The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is-
a) 20
b) 21
c) 22
d) 23

Explanation: Let the total number of workers be x.
8000x = (12000 × 7) + 6000(x - 7)
2000x = 42000
x = 21

9. The average age of a husband and his wife was 23 years at the times of their marriage. After five years they have a one-year old child. The average age of the family now is
a) 19 years
b) 23 years
c) 28.5 years
d) 29.3 years

Explanation: Sum of the present ages of husband, wife and child
= (23 × 2 + 5 × 2) + 1
= 57 years
Required average = $$\left( {\frac{{57}}{3}} \right)$$ = 19 years

10. In a class with a certain number of students, if one student weighting 50 kg is added then the average weight of the class increased by 1 kg. If one more student weighting 50 kg is added, then the average weight of the class increased by 1.5 kg over the original average. What is the original average weight (in kg) of the class?
a) 2
b) 4
c) 46
d) 47

\eqalign{ & \frac{{nx + 50}}{{n + 1}} = x + 1 \cr & nx + 50 = \left( {n + 1} \right)\left( {x + 1} \right) \cr & nx + 50 = nx + x + n + 1 \cr & x + n = 49 \cr & 2x + 2n = 98.....(i) \cr & {\text{And,}} \cr & \frac{{nx + 100}}{{n + 2}} = x + 1.5 \cr & nx + 100 = \left( {n + 2} \right)\left( {x + 1.5} \right) \cr & nx + 100 = nx + 1.5n + 2x + 3 \cr & 2x + 1.5n = 97.....(ii) \cr}