What is the average of the first 11 multiples of 9 ? Average (A.P. Based) Practice Set
Q) What is the average of the first 11 multiples of 9 ? (9ā§° āĻĒā§ā§°āĻĨāĻŽ 11āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒ: a) 119 b) 55 c) 54 d) 108
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
The first 11 multiples of 9 are:(9ā§° āĻĒā§ā§°āĻĨāĻŽ 11āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻ āĻšā§āĻā§): 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
Since these numbers form an Arithmetic Progression (A.P.), āĻ¯āĻŋāĻšā§āĻ¤ā§ āĻāĻ āĻ¸āĻāĻā§āĻ¯āĻžāĻŦā§ā§° āĻāĻāĻž Arithmetic Progression (A.P.) āĻāĻ āĻ¨ āĻā§°ā§,
Average = (First Term + Last Term) ÷ 2 (āĻāĻĄāĻŧ = (āĻĒā§ā§°āĻĨāĻŽ āĻĒāĻĻ + āĻļā§āĻˇ āĻĒāĻĻ) ÷ 2)
Average = 9 + 99 / 2 = 108 / 2 =
Shortcut / āĻāĻŽā§ āĻā§āĻļāĻ˛
For consecutive multiples, Average = Middle Term (āĻ§āĻžā§°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻā§āĻˇā§āĻ¤ā§ā§°āĻ¤, āĻāĻĄāĻŧ = āĻŽāĻžāĻā§° āĻĒāĻĻ)
The middle term of the 11 multiples is 54. (11āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻŽāĻžāĻā§° āĻĒāĻĻ āĻšā§āĻā§ 54āĨ¤)
Ans / āĻāĻ¤ā§āĻ¤ā§°: (c) 54
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Average (A.P. Based) Practice Set – Medium & Tough (āĻāĻĄāĻŧ (A.P. āĻāĻŋāĻ¤ā§āĻ¤āĻŋāĻ) āĻ āĻ¨ā§āĻļā§āĻ˛āĻ¨ā§ – āĻŽāĻ§ā§āĻ¯āĻŽ āĻā§°ā§ āĻāĻ āĻŋāĻ¨)
1. What is the average of the first 15 multiples of 8 ? (1. 8ā§° āĻĒā§ā§°āĻĨāĻŽ 15āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?)
A) 60 B) 64 C) 72 D) 80
2. What is the average of the first 21 multiples of 7 ? (2. 7ā§° āĻĒā§ā§°āĻĨāĻŽ 21āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?)
A) 70 B) 77 C) 84 D) 91
3. What is the average of the first 25 multiples of 12 ? 3. 12ā§° āĻĒā§ā§°āĻĨāĻŽ 25āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?
A) 144 B) 150 C) 156 D) 162
4. What is the average of all multiples of 5 from 5 to 95 ? 4. 5ā§° 5ā§° āĻĒā§°āĻž 95āĻ˛ā§ āĻ¸āĻāĻ˛ā§ āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨?
A) 45 B) 50 C) 55 D) 60
5. What is the average of the first 31 multiples of 4 ? 5. 4ā§° āĻĒā§ā§°āĻĨāĻŽ 31āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?
A) 60 B) 62 C) 64 D) 66
6. What is the average of all multiples of 9 from 18 to 180 ? 6. 9ā§° 18ā§° āĻĒā§°āĻž 180āĻ˛ā§ āĻ¸āĻāĻ˛ā§ āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?
A) 90 B) 95 C) 99 D) 102
7. The average of the first 19 multiples of a number is 95. Find the number. 7. āĻā§āĻ¨ā§ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻĒā§ā§°āĻĨāĻŽ 19āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ 95āĨ¤ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤
A) 8 B) 10 C) 12 D) 14
8. The average of the first 29 multiples of a number is 174. Find the number. 8. āĻā§āĻ¨ā§ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻĒā§ā§°āĻĨāĻŽ 29āĻāĻž āĻā§āĻŖāĻŋāĻ¤āĻā§° āĻāĻĄāĻŧ 174āĨ¤ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤
A) 10 B) 12 C) 14 D) 16
9. What is the average of all even numbers from 2 to 100 ? 9. 2ā§° āĻĒā§°āĻž 100āĻ˛ā§ āĻ¸āĻāĻ˛ā§ āĻ¯ā§āĻā§āĻŽ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?
A) 49 B) 50 C) 51 D) 52
10. What is the average of all odd numbers from 1 to 99 ? 10. 1ā§° āĻĒā§°āĻž 99āĻ˛ā§ āĻ¸āĻāĻ˛ā§ āĻŦāĻŋāĻˇāĻŽ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻāĻĄāĻŧ āĻāĻŋāĻŽāĻžāĻ¨ ?
A) 48 B) 49 C) 50 D) 51