Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 641 · 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.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹140 (d) ₹180
2. 2.If 8 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹27 (b) ₹216 (c) ₹25 (d) ₹30
3. 3.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 3 days (d) 15 days
4. 4.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 15 days (d) 11 days
5. 5.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹52 (b) ₹39 (c) ₹13 (d) ₹65
6. 6.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹259 (b) ₹296 (c) ₹37 (d) ₹148
7. 7.If 5 notebooks cost ₹55, how much do 4 notebooks cost? (a) ₹55 (b) ₹220 (c) ₹44 (d) ₹54
8. 8.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 43 days (c) 42 days (d) 8 days
9. 9.If 8 kites cost ₹40, how much do 2 kites cost? (a) ₹34 (b) ₹15 (c) ₹80 (d) ₹10
10. 10.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹145 (d) ₹87
11. 11.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹144 (d) ₹104
12. 12.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 4 days
13. 13.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹74 (d) ₹75
14. 14.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹230 (d) ₹138
15. 15.₹128 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹128 (b) ₹64 (c) ₹96 (d) ₹32
16. 16.₹294 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹210 (d) ₹84
17. 17.If 2 notebooks cost ₹34, how much do 3 notebooks cost? (a) ₹68 (b) ₹102 (c) ₹51 (d) ₹35
18. 18.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹5 (b) ₹45 (c) ₹35 (d) ₹25
19. 19.If 6 kites cost ₹66, how much do 4 kites cost? (a) ₹264 (b) ₹44 (c) ₹55 (d) ₹64
20. 20.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹50 (b) ₹275 (c) ₹350 (d) ₹200
21. 21.If 4 mangoes cost ₹20, how much do 8 mangoes cost? (a) ₹24 (b) ₹160 (c) ₹45 (d) ₹40
22. 22.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 2 days (d) 8 days
23. 23.If 2 pens cost ₹14, how much do 3 pens cost? (a) ₹15 (b) ₹21 (c) ₹42 (d) ₹28
24. 24.If 7 kites cost ₹21, how much do 11 kites cost? (a) ₹33 (b) ₹25 (c) ₹36 (d) ₹231
25. 25.If 4 notebooks cost ₹72, how much do 10 notebooks cost? (a) ₹78 (b) ₹720 (c) ₹180 (d) ₹198
26. 26.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 23 days (d) 7 days
27. 27.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹14 (b) ₹63 (c) ₹112 (d) ₹126
28. 28.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹164 (b) ₹82 (c) ₹41 (d) ₹123
29. 29.If 3 kites cost ₹45, how much do 10 kites cost? (a) ₹150 (b) ₹450 (c) ₹52 (d) ₹165
30. 30.If 3 pens cost ₹48, how much do 4 pens cost? (a) ₹64 (b) ₹80 (c) ₹192 (d) ₹49
31. 31.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 9 days (d) 13 days
32. 32.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 49 days (d) 19 days
33. 33.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹64 (b) ₹56 (c) ₹16 (d) ₹48
34. 34.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹168 (b) ₹120 (c) ₹216 (d) ₹24
35. 35.If 8 mangoes cost ₹152, how much do 5 mangoes cost? (a) ₹149 (b) ₹760 (c) ₹114 (d) ₹95
36. 36.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 8 days
37. 37.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹136 (b) ₹34 (c) ₹306 (d) ₹221
38. 38.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 6 days (d) 18 days
39. 39.If 4 pens cost ₹76, how much do 2 pens cost? (a) ₹38 (b) ₹57 (c) ₹152 (d) ₹74
40. 40.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 17 days (c) 34 days (d) 5 days

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