Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 223 · 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 ₹72, how much do 7 kites cost? (a) ₹76 (b) ₹504 (c) ₹192 (d) ₹168
2. 2.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 13 days (d) 8 days
3. 3.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 19 days (d) 17 days
4. 4.9 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) 15 days (d) 16 days
5. 5.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹64 (d) ₹128
6. 6.9 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
7. 7.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 4 days (d) 27 days
8. 8.If 3 mangoes cost ₹12, how much do 6 mangoes cost? (a) ₹28 (b) ₹24 (c) ₹72 (d) ₹15
9. 9.If 2 kites cost ₹44, how much do 10 kites cost? (a) ₹220 (b) ₹242 (c) ₹440 (d) ₹52
10. 10.If 8 notebooks cost ₹104, how much do 12 notebooks cost? (a) ₹156 (b) ₹1248 (c) ₹108 (d) ₹169
11. 11.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 18 days (d) 7 days
12. 12.If 2 kites cost ₹42, how much do 9 kites cost? (a) ₹378 (b) ₹49 (c) ₹189 (d) ₹210
13. 13.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹35 (c) ₹63 (d) ₹7
14. 14.If 8 kites cost ₹48, how much do 9 kites cost? (a) ₹54 (b) ₹60 (c) ₹49 (d) ₹432
15. 15.If 3 kites cost ₹24, how much do 12 kites cost? (a) ₹288 (b) ₹104 (c) ₹96 (d) ₹33
16. 16.If 7 notebooks cost ₹49, how much do 4 notebooks cost? (a) ₹35 (b) ₹196 (c) ₹46 (d) ₹28
17. 17.If 6 mangoes cost ₹60, how much do 3 mangoes cost? (a) ₹40 (b) ₹180 (c) ₹57 (d) ₹30
18. 18.If 8 pens cost ₹72, how much do 3 pens cost? (a) ₹36 (b) ₹216 (c) ₹27 (d) ₹67
19. 19.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹56 (b) ₹72 (c) ₹8 (d) ₹40
20. 20.If 7 pens cost ₹42, how much do 10 pens cost? (a) ₹45 (b) ₹420 (c) ₹66 (d) ₹60
21. 21.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹56 (b) ₹24 (c) ₹8 (d) ₹40
22. 22.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹72 (c) ₹84 (d) ₹12
23. 23.If 9 mangoes cost ₹81, how much do 2 mangoes cost? (a) ₹162 (b) ₹27 (c) ₹74 (d) ₹18
24. 24.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹140 (d) ₹175
25. 25.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 28 days (d) 18 days
26. 26.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹93 (d) ₹155
27. 27.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹162 (b) ₹81 (c) ₹18 (d) ₹144
28. 28.If 5 notebooks cost ₹25, how much do 11 notebooks cost? (a) ₹275 (b) ₹31 (c) ₹55 (d) ₹60
29. 29.If 7 mangoes cost ₹77, how much do 9 mangoes cost? (a) ₹79 (b) ₹110 (c) ₹693 (d) ₹99
30. 30.If 3 pens cost ₹42, how much do 4 pens cost? (a) ₹168 (b) ₹56 (c) ₹43 (d) ₹70
31. 31.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹144 (c) ₹24 (d) ₹168
32. 32.If 3 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹90 (b) ₹100 (c) ₹270 (d) ₹36
33. 33.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹343 (b) ₹49 (c) ₹245 (d) ₹294
34. 34.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹48 (c) ₹12 (d) ₹60
35. 35.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 15 days
36. 36.If 3 pens cost ₹72, how much do 11 pens cost? (a) ₹288 (b) ₹264 (c) ₹792 (d) ₹80
37. 37.If 6 mangoes cost ₹24, how much do 8 mangoes cost? (a) ₹36 (b) ₹192 (c) ₹32 (d) ₹26
38. 38.If 4 notebooks cost ₹64, how much do 3 notebooks cost? (a) ₹48 (b) ₹64 (c) ₹192 (d) ₹63
39. 39.If 6 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹35 (b) ₹28 (c) ₹168 (d) ₹40
40. 40.If 7 mangoes cost ₹105, how much do 5 mangoes cost? (a) ₹103 (b) ₹75 (c) ₹525 (d) ₹90

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