Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 622 · 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. 1.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 18 days (d) 19 days
2. 2.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹238 (b) ₹187 (c) ₹34 (d) ₹136
3. 3.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 5 days
4. 4.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 1 day (d) 9 days
5. 5.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹135 (c) ₹120 (d) ₹150
6. 6.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 8 days (d) 18 days
7. 7.If 6 pens cost ₹18, how much do 5 pens cost? (a) ₹18 (b) ₹15 (c) ₹17 (d) ₹90
8. 8.₹200 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹100 (b) ₹200 (c) ₹175 (d) ₹25
9. 9.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 7 days (d) 15 days
10. 10.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹175 (b) ₹50 (c) ₹200 (d) ₹150
11. 11.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 12 days
12. 12.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹48 (d) ₹56
13. 13.If 4 pens cost ₹32, how much do 5 pens cost? (a) ₹48 (b) ₹160 (c) ₹33 (d) ₹40
14. 14.If 4 pens cost ₹48, how much do 2 pens cost? (a) ₹96 (b) ₹36 (c) ₹24 (d) ₹46
15. 15.If 4 pens cost ₹92, how much do 8 pens cost? (a) ₹207 (b) ₹736 (c) ₹96 (d) ₹184
16. 16.If 4 pens cost ₹96, how much do 10 pens cost? (a) ₹240 (b) ₹960 (c) ₹264 (d) ₹102
17. 17.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
18. 18.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹261 (b) ₹232 (c) ₹233 (d) ₹29
19. 19.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 8 days (d) 5 days
20. 20.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 13 days (d) 12 days
21. 21.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹37 (b) ₹222 (c) ₹259 (d) ₹185
22. 22.If 3 kites cost ₹12, how much do 6 kites cost? (a) ₹28 (b) ₹72 (c) ₹15 (d) ₹24
23. 23.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹220 (b) ₹160 (c) ₹40 (d) ₹280
24. 24.If 6 kites cost ₹132, how much do 10 kites cost? (a) ₹136 (b) ₹242 (c) ₹220 (d) ₹1320
25. 25.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹72 (d) ₹8
26. 26.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 28 days (d) 19 days
27. 27.₹451 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹410 (b) ₹41 (c) ₹369 (d) ₹82
28. 28.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹47 (b) ₹141 (c) ₹235 (d) ₹188
29. 29.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 9 days (d) 8 days
30. 30.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹78 (d) ₹91
31. 31.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 14 days (c) 20 days (d) 16 days
32. 32.If 9 pens cost ₹63, how much do 10 pens cost? (a) ₹630 (b) ₹64 (c) ₹77 (d) ₹70
33. 33.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 5 days (d) 22 days
34. 34.₹130 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹65 (b) ₹130 (c) ₹104 (d) ₹26
35. 35.If 2 pens cost ₹14, how much do 5 pens cost? (a) ₹35 (b) ₹17 (c) ₹70 (d) ₹42
36. 36.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹70 (b) ₹63 (c) ₹28 (d) ₹7
37. 37.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹9 (d) ₹81
38. 38.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹99 (d) ₹110
39. 39.If 2 mangoes cost ₹44, how much do 5 mangoes cost? (a) ₹132 (b) ₹220 (c) ₹47 (d) ₹110
40. 40.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹66 (d) ₹55

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