Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 265 · 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.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹240 (b) ₹280 (c) ₹40 (d) ₹200
2. 2.If 9 pens cost ₹171, how much do 4 pens cost? (a) ₹166 (b) ₹76 (c) ₹95 (d) ₹684
3. 3.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹112 (b) ₹80 (c) ₹96 (d) ₹16
4. 4.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹50 (c) ₹10 (d) ₹30
5. 5.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 7 days
6. 6.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹130 (b) ₹169 (c) ₹26 (d) ₹208
7. 7.If 7 notebooks cost ₹161, how much do 4 notebooks cost? (a) ₹92 (b) ₹158 (c) ₹644 (d) ₹115
8. 8.If 6 pens cost ₹42, how much do 8 pens cost? (a) ₹44 (b) ₹336 (c) ₹56 (d) ₹63
9. 9.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 4 days (d) 3 days
10. 10.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹39 (b) ₹234 (c) ₹195 (d) ₹78
11. 11.If 3 kites cost ₹45, how much do 2 kites cost? (a) ₹90 (b) ₹30 (c) ₹45 (d) ₹44
12. 12.₹369 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹369 (b) ₹329 (c) ₹41 (d) ₹328
13. 13.If 8 pens cost ₹112, how much do 12 pens cost? (a) ₹116 (b) ₹1344 (c) ₹182 (d) ₹168
14. 14.If 6 notebooks cost ₹84, how much do 8 notebooks cost? (a) ₹672 (b) ₹126 (c) ₹86 (d) ₹112
15. 15.If 9 kites cost ₹216, how much do 10 kites cost? (a) ₹2160 (b) ₹264 (c) ₹240 (d) ₹217
16. 16.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹15 (c) ₹45 (d) ₹30
17. 17.If 7 notebooks cost ₹112, how much do 9 notebooks cost? (a) ₹160 (b) ₹1008 (c) ₹144 (d) ₹114
18. 18.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 7 days
19. 19.If 8 notebooks cost ₹136, how much do 9 notebooks cost? (a) ₹170 (b) ₹153 (c) ₹1224 (d) ₹137
20. 20.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 16 days (d) 8 days
21. 21.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 18 days (d) 3 days
22. 22.₹144 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹144 (c) ₹108 (d) ₹36
23. 23.If 6 notebooks cost ₹144, how much do 7 notebooks cost? (a) ₹168 (b) ₹192 (c) ₹1008 (d) ₹145
24. 24.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹31 (b) ₹310 (c) ₹279 (d) ₹155
25. 25.If 7 notebooks cost ₹168, how much do 9 notebooks cost? (a) ₹216 (b) ₹1512 (c) ₹240 (d) ₹170
26. 26.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹315 (c) ₹225 (d) ₹405
27. 27.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 31 days (c) 15 days (d) 30 days
28. 28.If 3 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹47 (b) ₹32 (c) ₹48 (d) ₹96
29. 29.If 8 notebooks cost ₹168, how much do 9 notebooks cost? (a) ₹169 (b) ₹210 (c) ₹1512 (d) ₹189
30. 30.₹329 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹141 (b) ₹188 (c) ₹235 (d) ₹47
31. 31.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
32. 32.If 6 notebooks cost ₹42, how much do 5 notebooks cost? (a) ₹41 (b) ₹35 (c) ₹210 (d) ₹42
33. 33.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 2 days (d) 13 days
34. 34.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 8 days (d) 6 days
35. 35.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 36 days (c) 15 days (d) 1 day
36. 36.If 7 kites cost ₹126, how much do 11 kites cost? (a) ₹198 (b) ₹130 (c) ₹216 (d) ₹1386
37. 37.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹344 (d) ₹387
38. 38.9 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
39. 39.If 3 notebooks cost ₹18, how much do 12 notebooks cost? (a) ₹27 (b) ₹216 (c) ₹78 (d) ₹72
40. 40.If 4 kites cost ₹88, how much do 11 kites cost? (a) ₹242 (b) ₹968 (c) ₹95 (d) ₹264

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