Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 81 · 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 8 kites cost ₹40, how much do 4 kites cost? (a) ₹36 (b) ₹20 (c) ₹25 (d) ₹160
2. 2.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 6 days (d) 7 days
3. 3.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹98 (b) ₹147 (c) ₹49 (d) ₹196
4. 4.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 17 days (c) 9 days (d) 39 days
5. 5.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 9 days
6. 6.₹441 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹343 (b) ₹49 (c) ₹392 (d) ₹98
7. 7.If 3 pens cost ₹66, how much do 11 pens cost? (a) ₹264 (b) ₹74 (c) ₹726 (d) ₹242
8. 8.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 10 days (d) 9 days
9. 9.If 7 mangoes cost ₹126, how much do 4 mangoes cost? (a) ₹123 (b) ₹90 (c) ₹504 (d) ₹72
10. 10.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹258 (d) ₹215
11. 11.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 1 day (d) 3 days
12. 12.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 18 days (d) 2 days
13. 13.If 3 mangoes cost ₹42, how much do 5 mangoes cost? (a) ₹44 (b) ₹84 (c) ₹70 (d) ₹210
14. 14.If 3 pens cost ₹42, how much do 11 pens cost? (a) ₹50 (b) ₹168 (c) ₹154 (d) ₹462
15. 15.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹189 (b) ₹168 (c) ₹21 (d) ₹63
16. 16.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
17. 17.If 2 mangoes cost ₹26, how much do 11 mangoes cost? (a) ₹143 (b) ₹156 (c) ₹286 (d) ₹35
18. 18.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
19. 19.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹90 (b) ₹117 (c) ₹18 (d) ₹144
20. 20.If 7 mangoes cost ₹21, how much do 12 mangoes cost? (a) ₹252 (b) ₹36 (c) ₹26 (d) ₹39
21. 21.If 4 notebooks cost ₹40, how much do 2 notebooks cost? (a) ₹20 (b) ₹30 (c) ₹80 (d) ₹38
22. 22.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 25 days (d) 24 days
23. 23.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹70 (d) ₹35
24. 24.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹288 (b) ₹48 (c) ₹264 (d) ₹240
25. 25.If 4 pens cost ₹88, how much do 10 pens cost? (a) ₹880 (b) ₹242 (c) ₹220 (d) ₹94
26. 26.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹45 (b) ₹40 (c) ₹5 (d) ₹41
27. 27.If 4 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹144 (b) ₹156 (c) ₹576 (d) ₹56
28. 28.₹126 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹18 (b) ₹54 (c) ₹63 (d) ₹72
29. 29.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 25 days (d) 24 days
30. 30.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 9 days (d) 49 days
31. 31.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 3 days (d) 4 days
32. 32.If 3 pens cost ₹42, how much do 8 pens cost? (a) ₹47 (b) ₹126 (c) ₹112 (d) ₹336
33. 33.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days
34. 34.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹90 (b) ₹65 (c) ₹10 (d) ₹40
35. 35.If 8 notebooks cost ₹128, how much do 9 notebooks cost? (a) ₹144 (b) ₹160 (c) ₹1152 (d) ₹129
36. 36.₹90 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹90 (d) ₹45
37. 37.If 9 notebooks cost ₹207, how much do 6 notebooks cost? (a) ₹1242 (b) ₹138 (c) ₹161 (d) ₹204
38. 38.If 2 kites cost ₹50, how much do 3 kites cost? (a) ₹100 (b) ₹51 (c) ₹75 (d) ₹150
39. 39.If 9 notebooks cost ₹171, how much do 6 notebooks cost? (a) ₹1026 (b) ₹133 (c) ₹168 (d) ₹114
40. 40.If 5 pens cost ₹100, how much do 6 pens cost? (a) ₹101 (b) ₹140 (c) ₹600 (d) ₹120

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