Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 872 · 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. 1.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 17 days
2. 2.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 18 days (d) 13 days
3. 3.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 17 days (d) 11 days
4. 4.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 3 days (d) 2 days
5. 5.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 48 days (d) 18 days
6. 6.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹6 (b) ₹27 (c) ₹48 (d) ₹54
7. 7.If 5 notebooks cost ₹70, how much do 7 notebooks cost? (a) ₹490 (b) ₹98 (c) ₹72 (d) ₹112
8. 8.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 10 days (d) 7 days
9. 9.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹264 (c) ₹297 (d) ₹99
10. 10.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹123 (b) ₹83 (c) ₹82 (d) ₹41
11. 11.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 20 days (d) 14 days
12. 12.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 1 day (c) 3 days (d) 17 days
13. 13.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 23 days (d) 13 days
14. 14.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹13 (d) ₹78
15. 15.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹135 (b) ₹75 (c) ₹15 (d) ₹105
16. 16.If 2 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹112 (b) ₹224 (c) ₹37 (d) ₹128
17. 17.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹160 (c) ₹32 (d) ₹192
18. 18.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 36 days (c) 4 days (d) 5 days
19. 19.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 12 days (d) 18 days
20. 20.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹52 (b) ₹40 (c) ₹8 (d) ₹64
21. 21.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 25 days (c) 16 days (d) 4 days
22. 22.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹153 (b) ₹17 (c) ₹68 (d) ₹170
23. 23.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹60 (b) ₹96 (c) ₹78 (d) ₹12
24. 24.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
25. 25.If 7 pens cost ₹49, how much do 2 pens cost? (a) ₹98 (b) ₹14 (c) ₹21 (d) ₹44
26. 26.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 15 days
27. 27.If 5 pens cost ₹25, how much do 11 pens cost? (a) ₹275 (b) ₹55 (c) ₹31 (d) ₹60
28. 28.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹126 (d) ₹99
29. 29.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹15 (d) ₹5
30. 30.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 10 days (d) 11 days
31. 31.If 4 mangoes cost ₹80, how much do 5 mangoes cost? (a) ₹400 (b) ₹81 (c) ₹100 (d) ₹120
32. 32.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 4 days (d) 12 days
33. 33.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 8 days
34. 34.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
35. 35.₹180 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹144 (d) ₹90
36. 36.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹52 (d) ₹26
37. 37.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹240 (d) ₹220
38. 38.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 10 days
39. 39.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹81 (c) ₹72 (d) ₹9
40. 40.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹78 (b) ₹104 (c) ₹26 (d) ₹91

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