Average

Ladakh Police Sub-Inspector · Mathematics · 56 practice questions with answers and explanations: 18 Easy, 36 Medium, 2 Hard.

Sample questions

Sample Easy question 1

The average of 5 consecutive odd numbers is 41. Find the largest number.

  1. 45
  2. 49
  3. 47
  4. 43
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Answer: A. The numbers are 37, 39, 41, 43, 45; the largest is 45.

Sample Easy question 2

Find the average of 7, 14, 21, 28 and 35.

  1. 21
  2. 18
  3. 19
  4. 20
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Answer: A. Sum = 105, average = 105/5 = 21.

Sample Easy question 3

The average height of 30 boys is 150 cm and of 20 girls is 140 cm. Find the average height of all 50 students.

  1. 146
  2. 145
  3. 147
  4. 144
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Answer: A. Combined average = (30×150 + 20×140)/50 = 7300/50 = 146 cm.

Sample Medium question 4

The average of x numbers is 23 and the average of y numbers is 36. If the average of all (x + y) numbers is 32, find the ratio x : y.

  1. 2 : 5
  2. 4 : 9
  3. 5 : 9
  4. 9 : 4
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Answer: B. Use the rule of alligation: x : y = (36 − 32) : (32 − 23) = 4 : 9 = 4 : 9.

Sample Medium question 5

The average of x numbers is 15 and the average of y numbers is 28. If the average of all (x + y) numbers is 23, find the ratio x : y.

  1. 8 : 5
  2. 5 : 9
  3. 5 : 8
  4. 3 : 4
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Answer: C. Use the rule of alligation: x : y = (28 − 23) : (23 − 15) = 5 : 8 = 5 : 8.

Sample Medium question 6

The average of x numbers is 30 and the average of y numbers is 45. If the average of all (x + y) numbers is 37, find the ratio x : y.

  1. 1 : 1
  2. 7 : 8
  3. 9 : 7
  4. 8 : 7
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Answer: D. Use the rule of alligation: x : y = (45 − 37) : (37 − 30) = 8 : 7 = 8 : 7.

Sample Hard question 7

The average of 12 numbers is 18. If the average of the first 7 is 20 and the average of the last 6 is 15, find the 7th number.

  1. 15
  2. 17
  3. 14
  4. 16
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Answer: B. Total of 12 = 216. First 7 total = 140, last 6 total = 90. 7th number is counted in both groups, so 140 + 90 - 216 = 14 — the 7th number is 14.

Sample Hard question 8

The average of 11 numbers is 50. The average of the first 6 is 49 and of the last 6 is 52. Find the 6th number.

  1. 55
  2. 54
  3. 56
  4. 57
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Answer: C. Sum of all 11 = 550, first 6 sum = 294, last 6 sum = 312. The 6th number is counted in both: 294 + 312 - 550 = 56.

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