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1. The average age of 50 students and a teacher is 25 years. When the teacher’s age is excluded, the average age decreases by 1 year. What is the age of the teacher?

65

75

74

64

Answer (b).

Total age of 50 students and 1 teacher = 25 x 51 = 1275
Total age of the students = 24 x 50 = 1200. { Average age reduces by 1 when teachers age is not included}
Therefore the age of the teacher is 1275 – 1200 = 75 years. Ans. (b)

2. Average weight of 3 men A, B and C is 80 kg. Another man D joins the group and the average now becomes 75 kg. If another man E, whose weight is 2 kg more than that of D, replaces A then the average weight of B, C, D and E becomes 77 kg. The weight of A is:

54 kg

60 kg

52 kg

64 kg.

Answer (a).

Total age of A + B + C = 80 x 3 = 240 kgs.
Total age of A + B + C + D = 75 x 4 = 300 kgs.
Weight of D = 300 – 240 = 60 kgs.
Also the weight of E (2 kgs more than D) = 62 kgs.
A is replaced by E
E + B + C + D = 77 x 4 = 308
Difference between ages of E and A is 308 – 300 = 8 kgs
A’s weight = 62 – 8 = 54 kgs
Weight of A = 54 kgs. Ans. (a)

3. In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years and 9 months, then the number of girls in the school is

450

150

250

350

Answer (b).

Total age of all the students is average age multiplied by total students.
⇒ 11 ¾ x 600 = 7050 — (1)
Let the total number of girls be A
Then, total number of boys = 600 – A
Total age of girls and boys = A x 11 and (600 – A) x 12 respectively
Therefore,
⇒ (11A) + (600 – A) x 12 = 7050
⇒ – A + 7200 + 7050
⇒ A = 7200 – 7050 = 150
Number of girls in school is 150. Ans. (b)

4. Average rainfall on Monday, Tuesday, Wednesday and Thursday is 420.5 cm and average on Tuesday, Wednesday, Thursday and Friday is 440.5 cm. If the ratio of rainfall for Monday and Friday is 20:21, find the rainfall in cm for Monday and Friday.

1800, 1890

1682, 1762

1700, 1400

1600, 1680

Answer (d).

Total rainfall from Monday to Thursday
M, T, W, Th = 420.5 x 4 = 1,682 cms. — (1)
Total rainfall from Tuesday to Friday
T, W, Th, Fr = 440.5 x 4 = 1762 cms — (2)
Subtracting equation (1) from (2)
Difference between rainfall of Fr and M = 1,762 – 1682 = 80cms
20 : 21 can be written in numbers as 20x : 21x
Therefore 21x – 20x = 80 ⇒ x = 80
Rainfall on Monday = 20 x 80 = 1600
Rainfall on Friday = 21 x 80 = 1680
1600 cms and 1680 cms. Ans (d)

5. A batsman makes a score of 58 runs in the 15th inning and thus increases his average by 3 runs. What is the average after 15th inning?

12

14

16

18

Answer (c).

Let the average score till 14th inning be x.
Therefore total score till 14th inning = 14x
Total score after 15th inning = 14x + 58
Average score after 15th inning = 14x + 58/15 —(1)
Average after 15th inning = x + 3. — (as per the question) (2)
Equating (1) and (2)
⇒ 14x + 58/15 = x + 3 ⇒ 15x – 14x = 58 – 45 ⇒ x = 13
Average after 15th inning = 13 + 3 = 16. Ans (c)

6. The average of 7 numbers is 8. If one number is added, their average is 9. Then the added number is

12

11

16

14

Answer (c).

Since, the average of 7 numbers = 8 their total = 8 x 7 = 56
One number is added then there are 8 numbers with the average 9.
Total of 8 numbers with average 9 = 8 x 9 = 72.
The added number is therefore:,
72 – 56 = 16. Ans. (c)

7. In a club, the average age of the members is 30 years, the average age of the male members is 34 years and that of the female members is 26 years. The percentage of male members is:

50%

60%

30%

40%

Answer (a).

Let the number of males members be X and female members be Y.
Then,
Total age of male members = 34 x X
Total age of female members = 26 x Y
Total age of all the members = (X + Y) x 30
⇒ 34X + 26Y = (X + Y) x 30
⇒ 34X + 26Y = 30X + 30Y
⇒ 4X = 4Y ⇒ X = Y
Percentage of Males is 50%. Ans. (a)

8. The average age of a jury of 5 is 40 years. If a member aged 35 resigns and a man aged 25 becomes a member, then the average age of the new jury is:

30

38

40

42

Answer (b).

Total of ages of jury of 5 = 40 x 5 = 200
A member resigns the total reduces = 200 – 35 = 165
When a new member joins, the total increases = 165 + 25 = 190
Average age of the new jury is
= 190/5
= 38. Answer (b).

9. Average of the runs made by Raju, Shyam and Hari is 7 less than that made by Shyam, Hari and Kishore. If Kishore’s score is 35, what is Raju’s score?

14

21

35

7.

Answer (a).

Let the average of runs scored by Raju (R), Shyam (S), Hari (H) be x
Then their total = R + S + H = 3x → (1)
Average runs scored by Shyam (S), Hari (H) and Kishore (K) is x + 7
Then their total = S + H + K = (x + 7) x 3 → (2)
Subtracting (1) from (2)
R – K = 3x – 3x – 21
Difference between scores of Kishore and Raju = 21
Since Kishore’s score is 35, Raju’s score is 35 – 21 = 14
Raju’s score = 14. Ans. (a)

10. The average age of a group of 30 boys is 12 years. When 2 new boys join them, the average increases by 1/4 year. What is the average age (in years) of the two new boys?

12

13

14

16

Answer (c).

Total of ages of 30 boys = 30 x 12 = 360.
Total of ages of 32 boys = 32 x 12.25 = 392.
Total of ages of 2 new boys = 392 – 360 = 32 years
Average age of 2 new boys = 32/2 years
16 years. Ans (d)

11. If the average of 10% of a number, 25% of that number, 50% of that number and 75% of that is 24, then the number will be

50

60

70

80

Answer (b)

Let the number be N.
∴ (0.1N + 0.25N + 0.5N + 0.75N)4 = 24
⇒ 1.6N/4 = 24
⇒ 1.6N = 96
⇒ N = 60

12. 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 the workers in the workshop is

20

21

22

23

Answer (b)

Let the total number of workers be W
Total salary of the workers = 8000W
Total salary of 7 technicians = 12000 x 7 = 84000
Total salary of others (W – 7) = 6000 x (W – 7)
∴ 8000W = 84000 + 6000W &ndash 42000
⇒ 2000W = 42000
⇒ W = 21

13. The average of 5 numbers is 27. If one number is excluded, the average becomes 25. The excluded number is

25

27

30

35

Answer (d)

The total of 5 numbers = 27 x 5 = 135
The total of 4 numbers = 25 x 4 = 100
Therefore the excluded number = 135 – 100 = 35