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71. 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:

Discuss
Solution:
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
100+x6=17
100 + X = 102
X = 102 - 100 = 2 years
72. 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:

Discuss
Solution:
Let the rest workers = x
Now, According to question,
(7 + x) × 8000 = 12000 × 7 + 6000x
56000 + 8000x = 84000 + 6000x
2000x = 28000
x = 14
So total number of worker
= 14 + 7
= 21
73. 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?

Discuss
Solution:
Required run rate=282−(3.2×10)40=25040=6.25
74. 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?

Discuss
Solution:
Required average = 67×2+35×2+6×32+2+3=134+70+187=2227=3157years
75. 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?

Discuss
Solution:
Total sale for 5 months
= Rs. (6435 + 6927 + 6855 + 7230 + 6562)
= Rs. 34009
Therefore Required sale
= Rs. [(6500 × 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991
76. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

Discuss
Solution:
Average of 20 numbers = 0
∴ Sum of 20 numbers (0 x 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a)
77. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

Discuss
Solution:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
78. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

Discuss
Solution:
Let the average age of the whole team by x years
∴ 11x - (26 + 29) = 9(x - 1)
⇒ 11x - 9x = 46
⇒ 2x = 46
⇒ x = 23
So, average age of the team is 23 years
79. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

Discuss
Solution:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get:  2(P + Q + R) = 33000  or   P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000
Therefore P's monthly income = Rs. 4000
80. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

Discuss
Solution:
Sum of the present ages of husband, wife and child
= (27 x 3 + 3 x 3) years
= 90 years
Sum of the present ages of wife and child
= (20 x 2 + 5 x 2) years
= 50 years
∴ Husband's present age
= (90 - 50) years
= 40 years

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