Quantitative Aptitude

Mean, Third and Fourth Proportional: Practice Questions with Answers

14 practice questions on Mean, Third and Fourth Proportional, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   The fourth proportional to 4, x and 15 is 30. Find x.

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   Answer: 8

   Solution:

   1. Set up: 4 : x = 15 : 30.
   2. Cross-multiply: 4 × 30 = 15 × x → 120 = 15x → x = 8.

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2. Q.2

   Find the fourth proportional to 6, 9 and 18.

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   Answer: 27

   Solution:

   1. Set up: 6 : 9 = 18 : x.
   2. Cross-multiply: x = (9 × 18) / 6 = 162 / 6 = 27.

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3. Q.3

   The mean proportional between 5 and some number N is 20. Find N.

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   Answer: 80

   Solution:

   1. Set up: 5 : 20 = 20 : N.
   2. Cross-multiply: 5N = 400, so N = 80.
   3. Check: the mean proportional of 5 and 80 is √(5 × 80) = √400 = 20. Matches.

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4. Q.4

   Find the mean proportional between 4 and 25.

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   Answer: 10

   Solution:

   1. Set up: 4 : x = x : 25.
   2. Cross-multiply: x² = 4 × 25 = 100, so x = √100 = 10.

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5. Q.5

   Find the third proportional to 6 and 12, and verify that 6, 12 and your answer form a geometric progression.

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   Answer: 24

   Solution:

   1. x = 12² / 6 = 144 / 6 = 24.
   2. Check as a GP: 12/6 = 2, and 24/12 = 2 — the same common ratio both times, confirming 6, 12, 24 is a genuine GP.

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6. Q.6

   Find the third proportional to 4 and 8.

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   Answer: 16

   Solution:

   1. Set up: 4 : 8 = 8 : x.
   2. Cross-multiply: x = 8² / 4 = 64 / 4 = 16.

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7. Q.7

   Find the fourth proportional to 3, 5 and 12.

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   Answer: 20

   Solution:

   1. Set up: 3 : 5 = 12 : x.
   2. Cross-multiply: x = (5 × 12) / 3 = 60 / 3 = 20.

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8. Q.8

   Find the third proportional to 7 and 21.

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   Answer: 63. x = 21²/7 = 441/7.

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9. Q.9

   Find the third proportional to 3 and 9, and verify 3, 9 and your answer form a geometric progression.

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   Answer: 27. Check: 9/3 = 3 and 27/9 = 3, the same ratio.

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10. Q.10

    Find the mean proportional between 9 and 16.

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    Answer: 12

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11. Q.11

    Find the fourth proportional to 2, 7 and 10.

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    Answer: 35

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12. Q.12

    The fourth proportional to 5, y and 12 is 36. Find y.

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    Answer: 15. 5:y = 12:36, so 5×36 = 12y.

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13. Q.13

    Find the third proportional to 5 and 10.

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    Answer: 20

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14. Q.14

    The mean proportional between 8 and some number N is 16. Find N.

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    Answer: 32. 8:16 = 16:N, so N = 256/8.

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