Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 200 · 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.If 4 mangoes cost ₹60, how much do 3 mangoes cost? (a) ₹59 (b) ₹180 (c) ₹45 (d) ₹60
2. 2.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 8 days (d) 9 days
3. 3.₹30 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹15 (d) ₹25
4. 4.If 8 kites cost ₹184, how much do 7 kites cost? (a) ₹1288 (b) ₹183 (c) ₹184 (d) ₹161
5. 5.If 2 mangoes cost ₹34, how much do 5 mangoes cost? (a) ₹37 (b) ₹170 (c) ₹102 (d) ₹85
6. 6.₹120 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹60 (b) ₹15 (c) ₹120 (d) ₹105
7. 7.₹275 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹25 (b) ₹100 (c) ₹200 (d) ₹175
8. 8.If 9 pens cost ₹198, how much do 10 pens cost? (a) ₹242 (b) ₹1980 (c) ₹199 (d) ₹220
9. 9.If 2 notebooks cost ₹50, how much do 3 notebooks cost? (a) ₹100 (b) ₹75 (c) ₹150 (d) ₹51
10. 10.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 13 days (d) 12 days
11. 11.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 7 days
12. 12.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 6 days (d) 20 days
13. 13.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 31 days (d) 30 days
14. 14.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹43 (b) ₹430 (c) ₹86 (d) ₹387
15. 15.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹392 (b) ₹147 (c) ₹441 (d) ₹49
16. 16.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹49 (b) ₹196 (c) ₹147 (d) ₹98
17. 17.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 7 days (d) 10 days
18. 18.₹135 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹108 (b) ₹135 (c) ₹27 (d) ₹109
19. 19.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹224 (d) ₹96
20. 20.If 7 pens cost ₹21, how much do 11 pens cost? (a) ₹36 (b) ₹25 (c) ₹33 (d) ₹231
21. 21.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 37 days (d) 36 days
22. 22.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 41 days (b) 20 days (c) 10 days (d) 40 days
23. 23.If 4 mangoes cost ₹16, how much do 7 mangoes cost? (a) ₹28 (b) ₹32 (c) ₹112 (d) ₹19
24. 24.If 8 notebooks cost ₹96, how much do 9 notebooks cost? (a) ₹864 (b) ₹120 (c) ₹97 (d) ₹108
25. 25.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹63 (c) ₹112 (d) ₹14
26. 26.If 3 mangoes cost ₹33, how much do 6 mangoes cost? (a) ₹77 (b) ₹36 (c) ₹66 (d) ₹198
27. 27.If 8 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹39 (b) ₹28 (c) ₹288 (d) ₹36
28. 28.If 2 kites cost ₹44, how much do 8 kites cost? (a) ₹176 (b) ₹198 (c) ₹50 (d) ₹352
29. 29.If 5 pens cost ₹35, how much do 3 pens cost? (a) ₹28 (b) ₹33 (c) ₹105 (d) ₹21
30. 30.If 6 pens cost ₹30, how much do 5 pens cost? (a) ₹30 (b) ₹150 (c) ₹29 (d) ₹25
31. 31.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹54 (b) ₹90 (c) ₹18 (d) ₹108
32. 32.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹180 (b) ₹36 (c) ₹144 (d) ₹162
33. 33.If 7 pens cost ₹28, how much do 11 pens cost? (a) ₹48 (b) ₹44 (c) ₹32 (d) ₹308
34. 34.If 2 kites cost ₹28, how much do 4 kites cost? (a) ₹112 (b) ₹30 (c) ₹70 (d) ₹56
35. 35.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹10 (c) ₹20 (d) ₹5
36. 36.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹185 (b) ₹222 (c) ₹148 (d) ₹37
37. 37.If 3 mangoes cost ₹66, how much do 7 mangoes cost? (a) ₹462 (b) ₹70 (c) ₹176 (d) ₹154
38. 38.If 8 notebooks cost ₹72, how much do 9 notebooks cost? (a) ₹90 (b) ₹648 (c) ₹81 (d) ₹73
39. 39.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 14 days (c) 33 days (d) 2 days
40. 40.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days

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