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1. The average of the first fifteen natural numbers is

Correct Answers :

[D]

Explanation :

Required average = (1 + 2 + 3 + … + 15)/15 = 120/15 = 8. Alternately you could use the formula for sum of the first n natural numbers as n (n + 1)/2 with n as 15. Then average = Sum/15 = (15 x 16/2)/ 15 = 8

2. The average of the first ten whole numbers is

Correct Answers :

[A]

Explanation :

Required average = (0 + 1 + 2 + … + 9)/10 = 45/10 = 4.5

3. The average of the first ten even numbers is

Correct Answers :

[D]

Explanation :

Required average = (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)/10 = 110/10 = 11. Alternately you could use the formula for sum of the first n even natural numbers as n (n + 1) with n as 10. Then average = Sum/10 = 10 x 11/10 = 11.

4. The average of the first ten odd numbers is

Correct Answers :

[B]

Explanation :

The sum of the first n odd numbers = n2. In this case n = 10 --> Sum = 10^{2} = 100. Required average = 100/10 = 10.

5. The average of the first ten prime numbers is

Correct Answers :

[D]

Explanation :

Required average = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29)/10 = 129/10 = 12.9.

6. The average of the first ten composite numbers is

Correct Answers :

[C]

Explanation :

Required average = (4 + 6 + 8 + 9 + 10 + 12 + 14+ 15 + 16 + 18)/10 = 112/10 = 11.2.

7. The average of the first ten prime numbers, which
are odd, is

Correct Answers :

[D]

Explanation :

Required average = (3 + 5 + 7 + 11 + 13 + 17 + 19+ 23 + 29 + 31)/10 = 158/10 = 15.8.

8. The average age of 13 boys and the principal is
10 years. When the principal’s age is excluded, the average age decreases by 2 year. What is the age of
the principal?

Correct Answers :

[B]

Explanation :

P = 14 x 10 – 13 x 8 = 140 –104 = 36

9. The average weight of 3 boys A, B and C is 74 kg.
Another boy D joins the group and the average now becomes 70 kg. If another boy E, whose weight is 3
kg more than that of D, replaces A then the average weight of B, C, D and E becomes 75 kg. The weight
of A is

Correct Answers :

[D]

Explanation :

D's weight = 4 x 70 – 3 x 74 = 280 – 222 = 58.
E's weight = 58 + 3 = 61.

Now, we know that A + B + C + D = 4 x 70 = 280
and B + C + D + E = 75 x 4 = 300. Hence, A's
weight is 20 kg less than E 's weight. A = 61 - 20= 41 kg.

10. The mean temperature of Monday to Wednesday was
35 °C and of Tuesday to Thursday was 30 °C. If the temperature on Thursday was ½ that of Monday, the
temperature on Thursday was

Correct Answers :

[B]

Explanation :

Monday + Tuesday + Wednesday = 3 x 35 = 105; Tuesday + Wednesday + Thursday = 3 x 30 = 90.Thus, Monday – Thursday = 15 and Thursday = Monday/2 --> Monday = 30 and Thursday= 15

11. Five years ago, the average age of *A*, *B* and *C* was
25 years and that of *B* and *C* 10 years ago was 20 years. *A*'s present age is

Correct Answers :

[A]

Explanation :

Total present age of A, B and C = 25 x 3 + 15 = 75+ 15 = 90.

Total present age of B and C = 20 x 2 + 20 = 60.A 's age = 90 – 60 = 30.

12. Ganguly has a certain average for 4 innings. In the
5th inning, he scores 40 runs thereby increasing his average by 4 runs. His new average is

Correct Answers :

[B]

Explanation :

4x + 40 = 5(x + 4) --> x = 20 (average after 4 innings).

Hence, new average = 20 + 4 = 24.

13. The average of the first six multiples of 5 is

Correct Answers :

[D]

Explanation :

(5+10+15+20+25+30)/6 = 105/6 = 17.5

14. There are three fractions *A*, *B* and *C*. If *A* = 1/5 and
*B* = 1/8 and the average of *A*, *B* and *C* is 1/10. What is the value of *C*?

Correct Answers :

[D]

Explanation :

1/5 + 1/8 + C = 3 x 1/10 --> C = –1/40.

15. The marks obtained by Alan in Mathematics, English
and Biology are respectively 90 out of 100, 70 out of 150 and 150 out of 200. Find his average
score in percent.

Correct Answers :

[B]

Explanation :

His total score is 90 + 70 + 150 = 310 out of 450. This works out to a percentage score of = 68.88%

16. The average monthly expenditure of a family was
Rs.2250 for the first 3 months, Rs.2150 for the next three months and Rs. 5750 for the next three months. Find
the average income of the family for the 9 months, if they save Rs.500 per month.

Correct Answers :

[B]

Explanation :

Average income over 9 months = [3 x (2250 + 500) + 3 x (2150 + 500) + 3 x (5750+500)]/9 = 3883.33

17. The average age of a family of 5 members is 20
years. If the age of the youngest member be 5 years, what was the average age of the family at the birth
of the youngest member?

Correct Answers :

[B]

Explanation :

Total age (at present) = 5 x 20 = 100 years. Total age of the family excluding the youngest member (for the remaining 5 people) = 100 –5 = 95. Average age of the other 4 people in the family = 95/4 years. 5 years ago their average age = 95/4 – 5 = 75/4 =18.75 years.

18. The average age of 5 persons in a group is increased
by 10 years when two men aged 30 years and 40 years are substituted by two women. Find the average
age (in years) of the two women.

Correct Answers :

[A]

Explanation :

If the average age of 5 persons has gone up by 10 years it means the total age has gone up by 50 years.Thus the total age of the two women would be: 30 + 40 + 50 = 120. Hence, their average age = 60 years.

19. The average temperature for Wednesday, Thursday
and Friday was 20 °C. The average for Thursday, Friday and Saturday was 21 °C. If the temperature
on Saturday was 22 °C, what was the temperature on Wednesday?

Correct Answers :

[A]

Explanation :

W + T + F = 60; T + F + S = 63 --> S – W = 3. Hence temperature on Wednesday = 22 – 3 = 19.

20. The speed of the train in going from Kanpur to
Lucknow is 60 km/hr while when coming back from Lucknow to Kanpur, its speed is 40 km/hr. Find the
average speed (in km/hr) during the whole journey.

Correct Answers :

[B]

Explanation :

Average speed =

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