Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 944 · 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 7 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 18 days (d) 6 days
2. 2.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹165 (c) ₹180 (d) ₹30
3. 3.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 52 days (c) 19 days (d) 7 days
4. 4.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 16 days (d) 15 days
5. 5.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹69 (b) ₹92 (c) ₹23 (d) ₹115
6. 6.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹54 (d) ₹63
7. 7.If 6 pens cost ₹114, how much do 2 pens cost? (a) ₹228 (b) ₹38 (c) ₹110 (d) ₹57
8. 8.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 27 days (d) 7 days
9. 9.If 4 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹36 (b) ₹48 (c) ₹144 (d) ₹47
10. 10.If 5 kites cost ₹115, how much do 6 kites cost? (a) ₹161 (b) ₹116 (c) ₹138 (d) ₹690
11. 11.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹22 (b) ₹176 (c) ₹66 (d) ₹121
12. 12.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 18 days (d) 10 days
13. 13.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹80 (c) ₹10 (d) ₹45
14. 14.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 5 days (d) 7 days
15. 15.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 15 days (c) 11 days (d) 27 days
16. 16.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 12 days (d) 9 days
17. 17.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 9 days (c) 16 days (d) 8 days
18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days
19. 19.₹246 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹246 (b) ₹123 (c) ₹41 (d) ₹205
20. 20.If 8 kites cost ₹160, how much do 3 kites cost? (a) ₹60 (b) ₹480 (c) ₹155 (d) ₹80
21. 21.If 9 pens cost ₹72, how much do 5 pens cost? (a) ₹40 (b) ₹48 (c) ₹360 (d) ₹68
22. 22.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹108 (b) ₹54 (c) ₹27 (d) ₹81
23. 23.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 7 days
24. 24.If 3 kites cost ₹33, how much do 10 kites cost? (a) ₹110 (b) ₹330 (c) ₹40 (d) ₹121
25. 25.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 13 days (d) 22 days
26. 26.If 9 mangoes cost ₹171, how much do 6 mangoes cost? (a) ₹133 (b) ₹1026 (c) ₹114 (d) ₹168
27. 27.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
28. 28.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹52 (b) ₹40 (c) ₹64 (d) ₹8
29. 29.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 6 days (d) 5 days
30. 30.If 2 pens cost ₹38, how much do 3 pens cost? (a) ₹57 (b) ₹39 (c) ₹114 (d) ₹76
31. 31.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹180 (b) ₹100 (c) ₹140 (d) ₹20
32. 32.If 3 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹140 (b) ₹64 (c) ₹420 (d) ₹160
33. 33.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹148 (b) ₹370 (c) ₹37 (d) ₹333
34. 34.If 3 mangoes cost ₹45, how much do 9 mangoes cost? (a) ₹405 (b) ₹135 (c) ₹150 (d) ₹51
35. 35.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 7 days (d) 4 days
36. 36.If 8 notebooks cost ₹184, how much do 12 notebooks cost? (a) ₹2208 (b) ₹188 (c) ₹299 (d) ₹276
37. 37.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹35 (d) ₹5
38. 38.If 3 pens cost ₹42, how much do 9 pens cost? (a) ₹126 (b) ₹48 (c) ₹378 (d) ₹140
39. 39.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 12 days (d) 18 days
40. 40.₹189 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹189 (b) ₹169 (c) ₹168 (d) ₹21

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