Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 937 · 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.₹224 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹128 (b) ₹96 (c) ₹112 (d) ₹32
2. 2.₹56 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹48 (d) ₹8
3. 3.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹210 (b) ₹378 (c) ₹294 (d) ₹42
4. 4.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 13 days (d) 22 days
5. 5.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹115 (d) ₹138
6. 6.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 25 days (c) 14 days (d) 24 days
7. 7.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 45 days (b) 23 days (c) 7 days (d) 5 days
8. 8.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 1 day (d) 3 days
9. 9.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 8 days (d) 10 days
10. 10.If 7 pens cost ₹98, how much do 8 pens cost? (a) ₹99 (b) ₹126 (c) ₹112 (d) ₹784
11. 11.If 2 kites cost ₹48, how much do 7 kites cost? (a) ₹336 (b) ₹192 (c) ₹53 (d) ₹168
12. 12.If 8 pens cost ₹200, how much do 5 pens cost? (a) ₹197 (b) ₹125 (c) ₹1000 (d) ₹150
13. 13.If 2 kites cost ₹14, how much do 5 kites cost? (a) ₹70 (b) ₹17 (c) ₹42 (d) ₹35
14. 14.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹84 (b) ₹63 (c) ₹105 (d) ₹21
15. 15.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 7 days (d) 16 days
16. 16.If 3 pens cost ₹36, how much do 11 pens cost? (a) ₹144 (b) ₹396 (c) ₹44 (d) ₹132
17. 17.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹39 (d) ₹13
18. 18.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹270 (b) ₹225 (c) ₹45 (d) ₹315
19. 19.If 2 mangoes cost ₹28, how much do 8 mangoes cost? (a) ₹34 (b) ₹112 (c) ₹126 (d) ₹224
20. 20.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹42 (d) ₹49
21. 21.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 21 days (d) 45 days
22. 22.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 3 days (d) 28 days
23. 23.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 1 day (d) 3 days
24. 24.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 9 days (d) 17 days
25. 25.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 25 days (d) 13 days
26. 26.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹40 (d) ₹30
27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 19 days (d) 3 days
28. 28.If 7 mangoes cost ₹91, how much do 12 mangoes cost? (a) ₹1092 (b) ₹169 (c) ₹156 (d) ₹96
29. 29.If 2 mangoes cost ₹10, how much do 10 mangoes cost? (a) ₹55 (b) ₹100 (c) ₹50 (d) ₹18
30. 30.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 9 days (d) 10 days
31. 31.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹235 (d) ₹423
32. 32.If 6 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹432 (b) ₹96 (c) ₹141 (d) ₹72
33. 33.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 5 days
34. 34.If 9 mangoes cost ₹162, how much do 6 mangoes cost? (a) ₹972 (b) ₹126 (c) ₹108 (d) ₹159
35. 35.If 3 pens cost ₹75, how much do 4 pens cost? (a) ₹76 (b) ₹300 (c) ₹125 (d) ₹100
36. 36.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 16 days (c) 41 days (d) 4 days
37. 37.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹52 (d) ₹39
38. 38.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 26 days (d) 28 days
39. 39.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
40. 40.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 5 days (d) 16 days

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