Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 694 · 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. 1.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 17 days (d) 7 days
2. 2.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 16 days (d) 13 days
3. 3.If 7 notebooks cost ₹63, how much do 4 notebooks cost? (a) ₹60 (b) ₹36 (c) ₹252 (d) ₹45
4. 4.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹16 (c) ₹64 (d) ₹104
5. 5.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 4 days
6. 6.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 15 days (d) 14 days
7. 7.If 5 kites cost ₹105, how much do 10 kites cost? (a) ₹231 (b) ₹1050 (c) ₹210 (d) ₹110
8. 8.If 2 pens cost ₹40, how much do 7 pens cost? (a) ₹140 (b) ₹45 (c) ₹160 (d) ₹280
9. 9.If 3 pens cost ₹39, how much do 12 pens cost? (a) ₹468 (b) ₹156 (c) ₹169 (d) ₹48
10. 10.If 3 notebooks cost ₹48, how much do 10 notebooks cost? (a) ₹176 (b) ₹55 (c) ₹480 (d) ₹160
11. 11.If 7 kites cost ₹56, how much do 4 kites cost? (a) ₹53 (b) ₹32 (c) ₹40 (d) ₹224
12. 12.If 9 pens cost ₹117, how much do 10 pens cost? (a) ₹1170 (b) ₹143 (c) ₹118 (d) ₹130
13. 13.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹450 (b) ₹350 (c) ₹250 (d) ₹50
14. 14.If 9 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹20 (b) ₹31 (c) ₹144 (d) ₹16
15. 15.If 3 mangoes cost ₹45, how much do 8 mangoes cost? (a) ₹120 (b) ₹360 (c) ₹135 (d) ₹50
16. 16.If 9 mangoes cost ₹108, how much do 2 mangoes cost? (a) ₹24 (b) ₹101 (c) ₹36 (d) ₹216
17. 17.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 10 days
18. 18.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹150 (b) ₹240 (c) ₹30 (d) ₹195
19. 19.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 45 days (d) 44 days
20. 20.If 5 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹48 (b) ₹41 (c) ₹56 (d) ₹240
21. 21.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹44 (d) ₹88
22. 22.If 2 mangoes cost ₹38, how much do 12 mangoes cost? (a) ₹48 (b) ₹228 (c) ₹247 (d) ₹456
23. 23.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹45 (b) ₹55 (c) ₹44 (d) ₹11
24. 24.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹225 (b) ₹200 (c) ₹250 (d) ₹50
25. 25.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹250 (b) ₹25 (c) ₹225 (d) ₹100
26. 26.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 12 days (d) 11 days
27. 27.If 4 kites cost ₹72, how much do 7 kites cost? (a) ₹504 (b) ₹144 (c) ₹126 (d) ₹75
28. 28.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 3 days (d) 18 days
29. 29.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹35 (d) ₹20
30. 30.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹148 (b) ₹185 (c) ₹111 (d) ₹37
31. 31.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹119 (b) ₹17 (c) ₹68 (d) ₹136
32. 32.If 7 notebooks cost ₹77, how much do 11 notebooks cost? (a) ₹121 (b) ₹81 (c) ₹847 (d) ₹132
33. 33.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 4 days (d) 3 days
34. 34.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹12 (d) ₹18
35. 35.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 1 day (d) 3 days
36. 36.If 4 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹74 (b) ₹108 (c) ₹126 (d) ₹432
37. 37.If 7 kites cost ₹119, how much do 2 kites cost? (a) ₹34 (b) ₹114 (c) ₹51 (d) ₹238
38. 38.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 17 days (d) 21 days
39. 39.If 3 kites cost ₹75, how much do 4 kites cost? (a) ₹125 (b) ₹300 (c) ₹76 (d) ₹100
40. 40.If 8 pens cost ₹24, how much do 5 pens cost? (a) ₹18 (b) ₹15 (c) ₹21 (d) ₹120

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