Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 507 · 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 notebooks cost ₹80, how much do 11 notebooks cost? (a) ₹880 (b) ₹87 (c) ₹240 (d) ₹220
2. 2.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹64 (c) ₹16 (d) ₹40
3. 3.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 13 days
4. 4.If 9 mangoes cost ₹216, how much do 4 mangoes cost? (a) ₹211 (b) ₹120 (c) ₹864 (d) ₹96
5. 5.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 23 days (d) 22 days
6. 6.If 3 pens cost ₹48, how much do 7 pens cost? (a) ₹52 (b) ₹128 (c) ₹336 (d) ₹112
7. 7.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 11 days (d) 5 days
8. 8.If 5 kites cost ₹75, how much do 6 kites cost? (a) ₹105 (b) ₹90 (c) ₹76 (d) ₹450
9. 9.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹12 (b) ₹66 (c) ₹36 (d) ₹96
10. 10.If 4 kites cost ₹68, how much do 3 kites cost? (a) ₹204 (b) ₹67 (c) ₹68 (d) ₹51
11. 11.If 2 kites cost ₹28, how much do 3 kites cost? (a) ₹56 (b) ₹29 (c) ₹42 (d) ₹84
12. 12.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹189 (b) ₹63 (c) ₹168 (d) ₹21
13. 13.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 6 days
14. 14.If 4 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹84 (b) ₹27 (c) ₹21 (d) ₹28
15. 15.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹10 (d) ₹30
16. 16.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 15 days (d) 8 days
17. 17.If 2 pens cost ₹42, how much do 5 pens cost? (a) ₹45 (b) ₹105 (c) ₹210 (d) ₹126
18. 18.If 2 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹60 (b) ₹80 (c) ₹120 (d) ₹41
19. 19.If 9 pens cost ₹63, how much do 3 pens cost? (a) ₹57 (b) ₹28 (c) ₹189 (d) ₹21
20. 20.If 2 pens cost ₹10, how much do 7 pens cost? (a) ₹70 (b) ₹40 (c) ₹15 (d) ₹35
21. 21.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 28 days (d) 27 days
22. 22.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹130 (b) ₹80 (c) ₹20 (d) ₹180
23. 23.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹84 (b) ₹14 (c) ₹77 (d) ₹70
24. 24.If 4 kites cost ₹48, how much do 10 kites cost? (a) ₹54 (b) ₹132 (c) ₹120 (d) ₹480
25. 25.If 6 kites cost ₹126, how much do 7 kites cost? (a) ₹882 (b) ₹168 (c) ₹127 (d) ₹147
26. 26.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹16 (b) ₹60 (c) ₹25 (d) ₹20
27. 27.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹287 (b) ₹246 (c) ₹41 (d) ₹205
28. 28.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 11 days (d) 21 days
29. 29.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹216 (b) ₹27 (c) ₹81 (d) ₹243
30. 30.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 10 days (c) 14 days (d) 6 days
31. 31.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 20 days (d) 11 days
32. 32.If 8 notebooks cost ₹96, how much do 6 notebooks cost? (a) ₹84 (b) ₹576 (c) ₹94 (d) ₹72
33. 33.If 5 kites cost ₹75, how much do 11 kites cost? (a) ₹825 (b) ₹180 (c) ₹81 (d) ₹165
34. 34.If 7 mangoes cost ₹112, how much do 8 mangoes cost? (a) ₹144 (b) ₹113 (c) ₹896 (d) ₹128
35. 35.₹405 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹361 (b) ₹45 (c) ₹360 (d) ₹405
36. 36.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹220 (b) ₹308 (c) ₹396 (d) ₹44
37. 37.If 2 notebooks cost ₹38, how much do 11 notebooks cost? (a) ₹418 (b) ₹209 (c) ₹228 (d) ₹47
38. 38.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 5 days
39. 39.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 2 days (d) 6 days
40. 40.If 3 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹60 (b) ₹46 (c) ₹180 (d) ₹75

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