Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 600 · 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.₹209 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹133 (b) ₹76 (c) ₹152 (d) ₹19
2. 2.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 10 days (d) 2 days
3. 3.₹246 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹123 (d) ₹246
4. 4.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 9 days
5. 5.If 7 pens cost ₹21, how much do 11 pens cost? (a) ₹36 (b) ₹231 (c) ₹25 (d) ₹33
6. 6.If 3 notebooks cost ₹51, how much do 7 notebooks cost? (a) ₹136 (b) ₹55 (c) ₹357 (d) ₹119
7. 7.If 6 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹91 (b) ₹48 (c) ₹84 (d) ₹504
8. 8.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹163 (b) ₹189 (c) ₹162 (d) ₹27
9. 9.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 2 days (d) 1 day
10. 10.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 11 days (d) 1 day
11. 11.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹50 (b) ₹5 (c) ₹45 (d) ₹20
12. 12.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹144 (d) ₹64
13. 13.If 9 mangoes cost ₹63, how much do 3 mangoes cost? (a) ₹57 (b) ₹28 (c) ₹21 (d) ₹189
14. 14.₹440 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹44 (b) ₹308 (c) ₹220 (d) ₹132
15. 15.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 16 days (c) 26 days (d) 10 days
16. 16.If 9 kites cost ₹27, how much do 3 kites cost? (a) ₹9 (b) ₹21 (c) ₹12 (d) ₹81
17. 17.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹60 (b) ₹35 (c) ₹70 (d) ₹10
18. 18.If 3 mangoes cost ₹36, how much do 2 mangoes cost? (a) ₹72 (b) ₹35 (c) ₹36 (d) ₹24
19. 19.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 6 days (d) 10 days
20. 20.If 6 notebooks cost ₹72, how much do 11 notebooks cost? (a) ₹77 (b) ₹144 (c) ₹792 (d) ₹132
21. 21.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹72 (b) ₹117 (c) ₹18 (d) ₹162
22. 22.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 15 days (d) 16 days
23. 23.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹6 (d) ₹18
24. 24.₹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
25. 25.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹80 (c) ₹50 (d) ₹10
26. 26.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
27. 27.If 7 pens cost ₹56, how much do 12 pens cost? (a) ₹672 (b) ₹104 (c) ₹96 (d) ₹61
28. 28.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹54 (d) ₹108
29. 29.If 8 notebooks cost ₹168, how much do 3 notebooks cost? (a) ₹63 (b) ₹84 (c) ₹163 (d) ₹504
30. 30.If 7 mangoes cost ₹140, how much do 11 mangoes cost? (a) ₹144 (b) ₹1540 (c) ₹240 (d) ₹220
31. 31.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 12 days
32. 32.If 7 kites cost ₹56, how much do 3 kites cost? (a) ₹168 (b) ₹24 (c) ₹32 (d) ₹52
33. 33.3 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) 7 days (d) 3 days
34. 34.If 2 pens cost ₹48, how much do 7 pens cost? (a) ₹168 (b) ₹336 (c) ₹53 (d) ₹192
35. 35.If 3 kites cost ₹69, how much do 4 kites cost? (a) ₹70 (b) ₹276 (c) ₹92 (d) ₹115
36. 36.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹40 (b) ₹160 (c) ₹80 (d) ₹120
37. 37.If 6 mangoes cost ₹90, how much do 11 mangoes cost? (a) ₹95 (b) ₹990 (c) ₹180 (d) ₹165
38. 38.If 3 pens cost ₹51, how much do 7 pens cost? (a) ₹119 (b) ₹55 (c) ₹357 (d) ₹136
39. 39.If 9 kites cost ₹198, how much do 12 kites cost? (a) ₹2376 (b) ₹286 (c) ₹201 (d) ₹264
40. 40.If 7 pens cost ₹35, how much do 8 pens cost? (a) ₹40 (b) ₹280 (c) ₹45 (d) ₹36

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