Ratio and Proportion: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 3)

Let the third proportional be c. Since a:b = b:c, we get 3:6 = 6:c. Cross-multiplying: 3 x c = 6 x 6 = 36. So c = 6²/3 = 36/3 = 12. Check: 3 x 12 = 36 and 6 x 6 = 36, which match.

Let the third proportional be c. Since a:b = b:c, we get 2:10 = 10:c. Cross-multiplying: 2 x c = 10 x 10 = 100. So c = 10²/2 = 100/2 = 50. Check: 2 x 50 = 100 and 10 x 10 = 100, which match.

Let the third proportional be c. Since a:b = b:c, we get 7:14 = 14:c. Cross-multiplying: 7 x c = 14 x 14 = 196. So c = 14²/7 = 196/7 = 28. Check: 7 x 28 = 196 and 14 x 14 = 196, which match.

Let the third proportional be c. Since a:b = b:c, we get 4:12 = 12:c. Cross-multiplying: 4 x c = 12 x 12 = 144. So c = 12²/4 = 144/4 = 36. Check: 4 x 36 = 144 and 12 x 12 = 144, which match.

Let the third proportional be c. Since a:b = b:c, we get 9:12 = 12:c. Cross-multiplying: 9 x c = 12 x 12 = 144. So c = 12²/9 = 144/9 = 16. Check: 9 x 16 = 144 and 12 x 12 = 144, which match.

Let the third proportional be c. Since a:b = b:c, we get 7:7 = 7:c. Cross-multiplying: 7 x c = 7 x 7 = 49. So c = 7²/7 = 49/7 = 7. Check: 7 x 7 = 49 and 7 x 7 = 49, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 5:10 = 12:d. Cross-multiplying: 5 x d = 10 x 12. So d = (10 x 12)/5 = 120/5 = 24. Check: 5 x 24 = 120 and 10 x 12 = 120, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 15:15 = 5:d. Cross-multiplying: 15 x d = 15 x 5. So d = (15 x 5)/15 = 75/15 = 5. Check: 15 x 5 = 75 and 15 x 5 = 75, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 10:12 = 5:d. Cross-multiplying: 10 x d = 12 x 5. So d = (12 x 5)/10 = 60/10 = 6. Check: 10 x 6 = 60 and 12 x 5 = 60, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 18:12 = 15:d. Cross-multiplying: 18 x d = 12 x 15. So d = (12 x 15)/18 = 180/18 = 10. Check: 18 x 10 = 180 and 12 x 15 = 180, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 2:20 = 11:d. Cross-multiplying: 2 x d = 20 x 11. So d = (20 x 11)/2 = 220/2 = 110. Check: 2 x 110 = 220 and 20 x 11 = 220, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 9:9 = 14:d. Cross-multiplying: 9 x d = 9 x 14. So d = (9 x 14)/9 = 126/9 = 14. Check: 9 x 14 = 126 and 9 x 14 = 126, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 20:20 = 16:d. Cross-multiplying: 20 x d = 20 x 16. So d = (20 x 16)/20 = 320/20 = 16. Check: 20 x 16 = 320 and 20 x 16 = 320, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 6:13 = 18:d. Cross-multiplying: 6 x d = 13 x 18. So d = (13 x 18)/6 = 234/6 = 39. Check: 6 x 39 = 234 and 13 x 18 = 234, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 2:18 = 6:d. Cross-multiplying: 2 x d = 18 x 6. So d = (18 x 6)/2 = 108/2 = 54. Check: 2 x 54 = 108 and 18 x 6 = 108, which match.

Let the fourth proportional be d. Since a:b = c:d, we get 2:15 = 2:d. Cross-multiplying: 2 x d = 15 x 2. So d = (15 x 2)/2 = 30/2 = 15. Check: 2 x 15 = 30 and 15 x 2 = 30, which match.

The ratio is 5:8:2, so let the common multiplier be x. The three shares are 5x, 8x, and 2x. Together they add to 15x, and this equals Rs. 345. So x = 345/15 = 23. The shares are 115, 184, and 46. The largest share is Rs. 184. Check: 115 + 184 + 46 = 345, which matches the total.

The ratio is 4:6:5, so let the common multiplier be x. The three shares are 4x, 6x, and 5x. Together they add to 15x, and this equals Rs. 525. So x = 525/15 = 35. The shares are 140, 210, and 175. The largest share is Rs. 210. Check: 140 + 210 + 175 = 525, which matches the total.

The ratio is 3:4:4, so let the common multiplier be x. The three shares are 3x, 4x, and 4x. Together they add to 11x, and this equals Rs. 121. So x = 121/11 = 11. The shares are 33, 44, and 44. The largest share is Rs. 44. Check: 33 + 44 + 44 = 121, which matches the total.

The ratio is 2:7:1, so let the common multiplier be x. The three shares are 2x, 7x, and 1x. Together they add to 10x, and this equals Rs. 190. So x = 190/10 = 19. The shares are 38, 133, and 19. The largest share is Rs. 133. Check: 38 + 133 + 19 = 190, which matches the total.

The ratio is 2:8:5, so let the common multiplier be x. The three shares are 2x, 8x, and 5x. Together they add to 15x, and this equals Rs. 135. So x = 135/15 = 9. The shares are 18, 72, and 45. The largest share is Rs. 72. Check: 18 + 72 + 45 = 135, which matches the total.

The ratio is 1:1:2, so let the common multiplier be x. The three shares are 1x, 1x, and 2x. Together they add to 4x, and this equals Rs. 108. So x = 108/4 = 27. The shares are 27, 27, and 54. The largest share is Rs. 54. Check: 27 + 27 + 54 = 108, which matches the total.

The ratio is 8:7:3, so let the common multiplier be x. The three shares are 8x, 7x, and 3x. Together they add to 18x, and this equals Rs. 396. So x = 396/18 = 22. The shares are 176, 154, and 66. The largest share is Rs. 176. Check: 176 + 154 + 66 = 396, which matches the total.

The ratio is 7:1:6, so let the common multiplier be x. The three shares are 7x, 1x, and 6x. Together they add to 14x, and this equals Rs. 462. So x = 462/14 = 33. The shares are 231, 33, and 198. The largest share is Rs. 231. Check: 231 + 33 + 198 = 462, which matches the total.

The ratio is 5:2, so let the common multiplier be x. The two shares are 5x and 2x. Together they add to 7x, and this equals Rs. 133. So x = 133/7 = 19. The shares are 5 x 19 = 95 and 2 x 19 = 38. The smaller share is Rs. 38. Check: 95 + 38 = 133, which matches the total.