Ratio and Proportion: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 4)

The ratio is 5:7, so let the common multiplier be x. The two shares are 5x and 7x. Together they add to 12x, and this equals Rs. 396. So x = 396/12 = 33. The shares are 5 x 33 = 165 and 7 x 33 = 231. The smaller share is Rs. 165. Check: 165 + 231 = 396, which matches the total.

The ratio is 3:4, so let the common multiplier be x. The two shares are 3x and 4x. Together they add to 7x, and this equals Rs. 301. So x = 301/7 = 43. The shares are 3 x 43 = 129 and 4 x 43 = 172. The smaller share is Rs. 129. Check: 129 + 172 = 301, which matches the total.

The ratio is 8:11, so let the common multiplier be x. The two shares are 8x and 11x. Together they add to 19x, and this equals Rs. 532. So x = 532/19 = 28. The shares are 8 x 28 = 224 and 11 x 28 = 308. The smaller share is Rs. 224. Check: 224 + 308 = 532, which matches the total.

The ratio is 11:9, so let the common multiplier be x. The two shares are 11x and 9x. Together they add to 20x, and this equals Rs. 900. So x = 900/20 = 45. The shares are 11 x 45 = 495 and 9 x 45 = 405. The smaller share is Rs. 405. Check: 495 + 405 = 900, which matches the total.

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

The ratio is 2:11, so let the common multiplier be x. The two shares are 2x and 11x. Together they add to 13x, and this equals Rs. 780. So x = 780/13 = 60. The shares are 2 x 60 = 120 and 11 x 60 = 660. The smaller share is Rs. 120. Check: 120 + 660 = 780, which matches the total.

The ratio is 2:9, so let the common multiplier be x. The two shares are 2x and 9x. Together they add to 11x, and this equals Rs. 594. So x = 594/11 = 54. The shares are 2 x 54 = 108 and 9 x 54 = 486. The smaller share is Rs. 108. Check: 108 + 486 = 594, which matches the total.

The ratio is 9:2, so let the common multiplier be x. The two shares are 9x and 2x. Together they add to 11x, and this equals Rs. 594. So x = 594/11 = 54. The shares are 9 x 54 = 486 and 2 x 54 = 108. The smaller share is Rs. 108. Check: 486 + 108 = 594, which matches the total.

The ratio is 10:9, so let the common multiplier be x. The two shares are 10x and 9x. Together they add to 19x, and this equals Rs. 874. So x = 874/19 = 46. The shares are 10 x 46 = 460 and 9 x 46 = 414. The smaller share is Rs. 414. Check: 460 + 414 = 874, which matches the total.

Convert Rs. 3.5 into paise: Rs. 1 = 100 paise, so Rs. 3.5 = 350 paise. Now compare 350 paise with 67 paise, giving the ratio 350:67. Their H.C.F. is 1. Dividing both terms by 1 gives 350:67. Check: 350 x 1 = 350 and 67 x 1 = 67.

Convert Rs. 2 into paise: Rs. 1 = 100 paise, so Rs. 2 = 200 paise. Now compare 200 paise with 57 paise, giving the ratio 200:57. Their H.C.F. is 1. Dividing both terms by 1 gives 200:57. Check: 200 x 1 = 200 and 57 x 1 = 57.

Convert Rs. 4.5 into paise: Rs. 1 = 100 paise, so Rs. 4.5 = 450 paise. Now compare 450 paise with 89 paise, giving the ratio 450:89. Their H.C.F. is 1. Dividing both terms by 1 gives 450:89. Check: 450 x 1 = 450 and 89 x 1 = 89.

Convert Rs. 2.5 into paise: Rs. 1 = 100 paise, so Rs. 2.5 = 250 paise. Now compare 250 paise with 52 paise, giving the ratio 250:52. Their H.C.F. is 2. Dividing both terms by 2 gives 125:26. Check: 125 x 2 = 250 and 26 x 2 = 52.

Convert Rs. 1 into paise: Rs. 1 = 100 paise, so Rs. 1 = 100 paise. Now compare 100 paise with 55 paise, giving the ratio 100:55. Their H.C.F. is 5. Dividing both terms by 5 gives 20:11. Check: 20 x 5 = 100 and 11 x 5 = 55.

Convert Rs. 2.25 into paise: Rs. 1 = 100 paise, so Rs. 2.25 = 225 paise. Now compare 225 paise with 72 paise, giving the ratio 225:72. Their H.C.F. is 9. Dividing both terms by 9 gives 25:8. Check: 25 x 9 = 225 and 8 x 9 = 72.

The ratio is 42:168. Find the H.C.F. of 42 and 168: it is 42. Divide both terms by 42: 42/42 = 1 and 168/42 = 4. So the simplest form is 1:4. Check: 1 and 4 share no common factor other than 1.

The ratio is 44:34. Find the H.C.F. of 44 and 34: it is 2. Divide both terms by 2: 44/2 = 22 and 34/2 = 17. So the simplest form is 22:17. Check: 22 and 17 share no common factor other than 1.

The ratio is 145:150. Find the H.C.F. of 145 and 150: it is 5. Divide both terms by 5: 145/5 = 29 and 150/5 = 30. So the simplest form is 29:30. Check: 29 and 30 share no common factor other than 1.

The ratio is 60:36. Find the H.C.F. of 60 and 36: it is 12. Divide both terms by 12: 60/12 = 5 and 36/12 = 3. So the simplest form is 5:3. Check: 5 and 3 share no common factor other than 1.

The ratio is 60:39. Find the H.C.F. of 60 and 39: it is 3. Divide both terms by 3: 60/3 = 20 and 39/3 = 13. So the simplest form is 20:13. Check: 20 and 13 share no common factor other than 1.

The ratio is 36:198. Find the H.C.F. of 36 and 198: it is 18. Divide both terms by 18: 36/18 = 2 and 198/18 = 11. So the simplest form is 2:11. Check: 2 and 11 share no common factor other than 1.

The ratio is 102:162. Find the H.C.F. of 102 and 162: it is 6. Divide both terms by 6: 102/6 = 17 and 162/6 = 27. So the simplest form is 17:27. Check: 17 and 27 share no common factor other than 1.

The ratio is 168:140. Find the H.C.F. of 168 and 140: it is 28. Divide both terms by 28: 168/28 = 6 and 140/28 = 5. So the simplest form is 6:5. Check: 6 and 5 share no common factor other than 1.

The ratio is 437:152. Find the H.C.F. of 437 and 152: it is 19. Divide both terms by 19: 437/19 = 23 and 152/19 = 8. So the simplest form is 23:8. Check: 23 and 8 share no common factor other than 1.

The ratio is 360:180. Find the H.C.F. of 360 and 180: it is 180. Divide both terms by 180: 360/180 = 2 and 180/180 = 1. So the simplest form is 2:1. Check: 2 and 1 share no common factor other than 1.