Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 349 · 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 3 kites cost ₹39, how much do 4 kites cost? (a) ₹40 (b) ₹156 (c) ₹65 (d) ₹52
2. 2.If 9 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹35 (b) ₹32 (c) ₹288 (d) ₹36
3. 3.If 2 pens cost ₹36, how much do 8 pens cost? (a) ₹42 (b) ₹288 (c) ₹144 (d) ₹162
4. 4.If 5 pens cost ₹85, how much do 6 pens cost? (a) ₹86 (b) ₹510 (c) ₹119 (d) ₹102
5. 5.If 2 pens cost ₹18, how much do 12 pens cost? (a) ₹108 (b) ₹117 (c) ₹28 (d) ₹216
6. 6.If 6 kites cost ₹90, how much do 8 kites cost? (a) ₹120 (b) ₹135 (c) ₹720 (d) ₹92
7. 7.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹147 (b) ₹105 (c) ₹21 (d) ₹189
8. 8.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 8 days (d) 10 days
9. 9.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹91 (c) ₹90 (d) ₹135
10. 10.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹32 (c) ₹192 (d) ₹160
11. 11.₹140 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹20 (b) ₹70 (c) ₹140 (d) ₹120
12. 12.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 2 days (d) 8 days
13. 13.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 1 day (d) 10 days
14. 14.If 6 pens cost ₹150, how much do 12 pens cost? (a) ₹1800 (b) ₹325 (c) ₹156 (d) ₹300
15. 15.If 3 notebooks cost ₹18, how much do 11 notebooks cost? (a) ₹198 (b) ₹26 (c) ₹72 (d) ₹66
16. 16.If 7 notebooks cost ₹56, how much do 12 notebooks cost? (a) ₹61 (b) ₹672 (c) ₹104 (d) ₹96
17. 17.₹170 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹119 (d) ₹51
18. 18.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹126 (b) ₹72 (c) ₹18 (d) ₹144
19. 19.If 7 pens cost ₹56, how much do 2 pens cost? (a) ₹112 (b) ₹24 (c) ₹16 (d) ₹51
20. 20.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹306 (b) ₹34 (c) ₹340 (d) ₹170
21. 21.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 17 days
22. 22.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹270 (b) ₹195 (c) ₹120 (d) ₹30
23. 23.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
24. 24.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 20 days (d) 5 days
25. 25.If 3 pens cost ₹54, how much do 10 pens cost? (a) ₹180 (b) ₹198 (c) ₹61 (d) ₹540
26. 26.If 6 pens cost ₹42, how much do 9 pens cost? (a) ₹45 (b) ₹378 (c) ₹70 (d) ₹63
27. 27.If 2 notebooks cost ₹18, how much do 9 notebooks cost? (a) ₹90 (b) ₹81 (c) ₹162 (d) ₹25
28. 28.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 6 days (d) 5 days
29. 29.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 28 days
30. 30.If 5 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹56 (b) ₹48 (c) ₹41 (d) ₹240
31. 31.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹108 (b) ₹96 (c) ₹24 (d) ₹120
32. 32.If 8 notebooks cost ₹64, how much do 3 notebooks cost? (a) ₹24 (b) ₹32 (c) ₹192 (d) ₹59
33. 33.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 24 days (d) 4 days
34. 34.If 9 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹62 (b) ₹63 (c) ₹56 (d) ₹504
35. 35.If 7 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹129 (b) ₹1260 (c) ₹180 (d) ₹198
36. 36.If 2 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹84 (b) ₹42 (c) ₹56 (d) ₹29
37. 37.If 7 pens cost ₹98, how much do 6 pens cost? (a) ₹97 (b) ₹98 (c) ₹588 (d) ₹84
38. 38.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹26 (b) ₹169 (c) ₹208 (d) ₹130
39. 39.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹294 (d) ₹343
40. 40.If 8 kites cost ₹88, how much do 9 kites cost? (a) ₹89 (b) ₹99 (c) ₹110 (d) ₹792

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