Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 151 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹306 (b) ₹153 (c) ₹272 (d) ₹34
2. 2.If 4 kites cost ₹80, how much do 8 kites cost? (a) ₹180 (b) ₹640 (c) ₹84 (d) ₹160
3. 3.₹140 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹56 (d) ₹28
4. 4.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 16 days (d) 15 days
5. 5.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹126 (b) ₹18 (c) ₹108 (d) ₹63
6. 6.If 2 pens cost ₹34, how much do 3 pens cost? (a) ₹35 (b) ₹68 (c) ₹102 (d) ₹51
7. 7.₹63 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹9 (b) ₹54 (c) ₹55 (d) ₹63
8. 8.If 7 kites cost ₹77, how much do 4 kites cost? (a) ₹55 (b) ₹44 (c) ₹74 (d) ₹308
9. 9.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹63 (d) ₹56
10. 10.If 9 mangoes cost ₹108, how much do 6 mangoes cost? (a) ₹648 (b) ₹105 (c) ₹84 (d) ₹72
11. 11.If 2 pens cost ₹12, how much do 6 pens cost? (a) ₹42 (b) ₹72 (c) ₹36 (d) ₹16
12. 12.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹31 (b) ₹279 (c) ₹310 (d) ₹155
13. 13.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 3 days (d) 4 days
14. 14.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹294 (b) ₹245 (c) ₹49 (d) ₹196
15. 15.If 4 mangoes cost ₹76, how much do 11 mangoes cost? (a) ₹228 (b) ₹836 (c) ₹83 (d) ₹209
16. 16.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 8 days (d) 9 days
17. 17.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 6 days (d) 18 days
18. 18.If 9 mangoes cost ₹27, how much do 6 mangoes cost? (a) ₹21 (b) ₹18 (c) ₹162 (d) ₹24
19. 19.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 13 days (d) 9 days
20. 20.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹120 (d) ₹135
21. 21.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹54 (b) ₹36 (c) ₹27 (d) ₹19
22. 22.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 7 days (d) 8 days
23. 23.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 3 days (d) 5 days
24. 24.₹306 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹153 (b) ₹34 (c) ₹68 (d) ₹238
25. 25.If 6 pens cost ₹126, how much do 9 pens cost? (a) ₹1134 (b) ₹129 (c) ₹189 (d) ₹210
26. 26.If 9 notebooks cost ₹54, how much do 10 notebooks cost? (a) ₹60 (b) ₹55 (c) ₹540 (d) ₹66
27. 27.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 7 days (d) 17 days
28. 28.If 5 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹44 (b) ₹72 (c) ₹360 (d) ₹80
29. 29.If 7 notebooks cost ₹119, how much do 12 notebooks cost? (a) ₹124 (b) ₹204 (c) ₹221 (d) ₹1428
30. 30.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 19 days (d) 9 days
31. 31.If 9 pens cost ₹90, how much do 12 pens cost? (a) ₹130 (b) ₹93 (c) ₹1080 (d) ₹120
32. 32.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹150 (d) ₹175
33. 33.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 34 days (d) 17 days
34. 34.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹187 (b) ₹136 (c) ₹238 (d) ₹34
35. 35.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 7 days (d) 8 days
36. 36.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 1 day (c) 3 days (d) 9 days
37. 37.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹168 (b) ₹294 (c) ₹336 (d) ₹42
38. 38.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹24 (b) ₹84 (c) ₹12 (d) ₹54
39. 39.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹36 (c) ₹72 (d) ₹24
40. 40.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 17 days

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