Averages – II

1)In a family of 10 members, the average age of the family at present is 40 while the age of the youngest member in the family is 9 years. Find the average age of the family at the time of her birth?

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Sum of ages = 40 x 10 = 400
At the time of birth, i.e., 9 years back,
\({400-(10×9) \over {9}}\) = 34.4. Hence, (a).

2)The average age of 6 children of a family is 12 years but if we include the age of father and mother then the average age becomes 24 years. It is given that father’s age is 4 years more than the mother. Find the present age of mother.

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Sum of age of children = 72
72 + M+ F = 24 x 8 = 192.
M + F = 120 and F = M + 4
On solving both the equations we get, M = 58. Hence, (c).

3)The average marks secured by 20 students are 60 and later it was found that one entry is wrong and instead of 35 it was written as 55. What is the corrected average?

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\({(20×60)-55+35 \over {20}}\) = 59. Hence, (b).

4)The average marks obtained by 50 candidates in an examination are 25. If the average marks of the passed students are 30 while the average marks of the failed students is 20. Then how many number of students failed in the examination.

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Let P denote the number of students passed and F denote the number of students who failed.
50 x 25 = 30P + 20F and P + F = 50
On solving both the equations we get, F = 25. Hence, (d).

5)The average age of the class is 12 years. The average age of boys and girls is 10 and 14 years respectively. If the number of girls in the class is 20 then how many boys are there in the class?

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Let B denote the number of boys and G denote the number of girls.
10B + (14 × 20) = 12 × (20 + B)
On solving the above equation, we get, B = 20. Hence, (b).

6)2 years ago, the average age of Pritham, Naren, and Manu was 32 years. Also 4 years ago, the average age of Naren and Manu was 26 years. Find the present age of Pritham.

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Sum of ages of P + N + M 2 yrs ago = 32 × 2 = 64
So after 2 yrs, i.e. at present their total = 64 + (2 × 2) = 68
Similarly, sum of present age of N and M = (26 × 2) + (4 × 2) = 60
Therefore, present age of Pritham = 68 – 60 = 8. Hence, (c).

7)The average of 7 numbers is 50. Average of first four and last two is 30 and 40 respectively. Find the middle number.

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(50 × 8) – [(30 × 4) + (40 × 2)] = 200. Hence, (b).

8)While calculating the weight of a group of boys, the weight of one of the member was mistakenly written as 32 kg instead of 22 kg. Due to this the average of the weights increased by one kg. Find the number of boys in the group?

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Let x be the number of boys in the group.
(32 – 22) = \({x \over {2}}\)
Therefore, x = 20. Hence, (d).

9)In a class, the average marks secured by number of students in Mathematics is 45.25. 20% of students placed in category B made the average of 36 marks, while 25% who were placed in category A made the average of 60 marks. What is the average mark of the remaining students?

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Assume there are 100 students in the class, then in category A = 25 students, in B = 20 students, remaining = 55 students. Let x be the average of these 55 students.
Therefore, (20 × 36) + (25 × 60) + (55 × x) = 45 × 100 = 41.45. Hence, (a).

10)Two years ago the average age of daughter and mother was 48 yrs. Find their average age at present.

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Average age of D and M age 2 yrs ago = 48
Present average age of D and M = 48 + 2 = 50. Hence, (c).

11)The average age of 20 men is 50 yrs. If 10 new men of average age 40 yrs join them, then find the new average age.

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20 men age = 20 × 50 =1000
10 men age = 10 × 40 = 400
New average age = \({1000+400 \over {30}}\) = 46.67. Hence, (b).

12)The average salary of 90 employees in the bank is Rs.20,000 per month. If the number of clerk is twice the number of officer’s and average salary of clerk is halfof the average salary of officer, then find the average salary of officers.

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90 = 1:2 = 30:60 = Officer : Clerk
90 × 20000 = (30 × x) + (60 × \({x \over {2}}\))
18,00,000 = 60x
x = 30000. Hence, (a).

13)The average age of a group of peoples going for tour to Goa is 24 years. 20 new persons with an average age of 15 years join the group and their average age becomes 18 years. Find the number of persons initially going for tour.

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Initial number of persons = x
= 24x + (20 × 15) – 18(x + 20)
6x = 60
x = 10. Hence, (d).

14)The average presence of students of a class in a school on Monday, Tuesday and Wednesday is 40 and on the Wednesday, Thursday, Friday and Saturday is 36. If the average number of students on all the six days is 30, then find the number of students who attended the class on Thursday.

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(40 × 3) + (36 × 3)(30 × 6) = 120 + 108 – 180 = 48. Hence, (b).

15)The average weight of 6 persons increases by 2 kg. When a new person comes in place of one them weighing 48 kg, find the weight of the new person.

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Total weight increased = (6 x 2) kg = 12 kg
Weight of new person = (48 + 12) kg = 60 kg. Hence, (d).