Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 504 · 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.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹49 (b) ₹28 (c) ₹56 (d) ₹7
2. 2.₹162 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹18 (b) ₹81 (c) ₹126 (d) ₹36
3. 3.If 3 kites cost ₹39, how much do 9 kites cost? (a) ₹45 (b) ₹130 (c) ₹117 (d) ₹351
4. 4.If 6 pens cost ₹108, how much do 3 pens cost? (a) ₹324 (b) ₹54 (c) ₹72 (d) ₹105
5. 5.If 7 notebooks cost ₹21, how much do 10 notebooks cost? (a) ₹210 (b) ₹24 (c) ₹33 (d) ₹30
6. 6.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹91 (b) ₹78 (c) ₹65 (d) ₹13
7. 7.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 11 days (d) 26 days
8. 8.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹156 (b) ₹195 (c) ₹234 (d) ₹39
9. 9.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹6 (b) ₹15 (c) ₹18 (d) ₹12
10. 10.If 3 pens cost ₹63, how much do 9 pens cost? (a) ₹210 (b) ₹189 (c) ₹69 (d) ₹567
11. 11.If 8 notebooks cost ₹80, how much do 12 notebooks cost? (a) ₹960 (b) ₹84 (c) ₹130 (d) ₹120
12. 12.If 2 kites cost ₹46, how much do 4 kites cost? (a) ₹184 (b) ₹115 (c) ₹92 (d) ₹48
13. 13.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹40 (c) ₹200 (d) ₹240
14. 14.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 5 days (d) 35 days
15. 15.If 5 mangoes cost ₹45, how much do 10 mangoes cost? (a) ₹450 (b) ₹99 (c) ₹50 (d) ₹90
16. 16.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 3 days (d) 27 days
17. 17.₹516 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹215 (b) ₹43 (c) ₹301 (d) ₹258
18. 18.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹33 (d) ₹11
19. 19.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 5 days (d) 4 days
20. 20.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 19 days (d) 7 days
21. 21.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹144 (b) ₹60 (c) ₹37 (d) ₹48
22. 22.If 7 notebooks cost ₹161, how much do 11 notebooks cost? (a) ₹1771 (b) ₹253 (c) ₹276 (d) ₹165
23. 23.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹95 (d) ₹114
24. 24.If 7 mangoes cost ₹56, how much do 8 mangoes cost? (a) ₹448 (b) ₹72 (c) ₹57 (d) ₹64
25. 25.If 4 notebooks cost ₹68, how much do 5 notebooks cost? (a) ₹102 (b) ₹85 (c) ₹69 (d) ₹340
26. 26.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹240 (b) ₹288 (c) ₹48 (d) ₹144
27. 27.If 7 notebooks cost ₹119, how much do 3 notebooks cost? (a) ₹357 (b) ₹68 (c) ₹115 (d) ₹51
28. 28.If 9 kites cost ₹126, how much do 5 kites cost? (a) ₹122 (b) ₹630 (c) ₹84 (d) ₹70
29. 29.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹98 (b) ₹77 (c) ₹14 (d) ₹56
30. 30.If 3 kites cost ₹60, how much do 4 kites cost? (a) ₹61 (b) ₹80 (c) ₹240 (d) ₹100
31. 31.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 8 days (d) 6 days
32. 32.If 9 pens cost ₹144, how much do 10 pens cost? (a) ₹1440 (b) ₹176 (c) ₹160 (d) ₹145
33. 33.If 3 pens cost ₹42, how much do 9 pens cost? (a) ₹126 (b) ₹378 (c) ₹48 (d) ₹140
34. 34.If 9 notebooks cost ₹63, how much do 3 notebooks cost? (a) ₹189 (b) ₹57 (c) ₹28 (d) ₹21
35. 35.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 15 days (d) 4 days
36. 36.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 9 days
37. 37.If 3 pens cost ₹36, how much do 11 pens cost? (a) ₹132 (b) ₹44 (c) ₹396 (d) ₹144
38. 38.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹378 (b) ₹294 (c) ₹42 (d) ₹210
39. 39.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹96 (b) ₹60 (c) ₹120 (d) ₹24
40. 40.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 14 days

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