Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 986 · 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. 1.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 1 day
2. 2.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹153 (b) ₹170 (c) ₹34 (d) ₹136
3. 3.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹126 (b) ₹18 (c) ₹63 (d) ₹108
4. 4.If 4 kites cost ₹96, how much do 5 kites cost? (a) ₹97 (b) ₹120 (c) ₹480 (d) ₹144
5. 5.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 4 days
6. 6.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹136 (d) ₹153
7. 7.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹79 (d) ₹117
8. 8.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹92 (b) ₹69 (c) ₹115 (d) ₹23
9. 9.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 1 day
10. 10.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 11 days (d) 17 days
11. 11.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹31 (b) ₹62 (c) ₹155 (d) ₹186
12. 12.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹24 (b) ₹216 (c) ₹168 (d) ₹120
13. 13.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 3 days (d) 5 days
14. 14.If 9 notebooks cost ₹207, how much do 3 notebooks cost? (a) ₹92 (b) ₹69 (c) ₹621 (d) ₹201
15. 15.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 20 days (c) 21 days (d) 19 days
16. 16.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹228 (b) ₹38 (c) ₹190 (d) ₹114
17. 17.If 9 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹162 (b) ₹18 (c) ₹24 (d) ₹48
18. 18.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹44 (d) ₹48
19. 19.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 6 days (d) 7 days
20. 20.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹40 (d) ₹25
21. 21.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹47 (b) ₹94 (c) ₹188 (d) ₹141
22. 22.If 3 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹144 (b) ₹48 (c) ₹54 (d) ₹23
23. 23.If 2 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹273 (b) ₹504 (c) ₹252 (d) ₹52
24. 24.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 17 days (c) 35 days (d) 11 days
25. 25.If 4 pens cost ₹28, how much do 7 pens cost? (a) ₹196 (b) ₹56 (c) ₹31 (d) ₹49
26. 26.If 4 mangoes cost ₹56, how much do 7 mangoes cost? (a) ₹59 (b) ₹392 (c) ₹98 (d) ₹112
27. 27.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 27 days (d) 28 days
28. 28.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹282 (b) ₹235 (c) ₹188 (d) ₹47
29. 29.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 11 days (d) 36 days
30. 30.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹64 (b) ₹36 (c) ₹72 (d) ₹8
31. 31.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 11 days (d) 2 days
32. 32.If 8 mangoes cost ₹152, how much do 10 mangoes cost? (a) ₹1520 (b) ₹209 (c) ₹190 (d) ₹154
33. 33.If 4 pens cost ₹24, how much do 11 pens cost? (a) ₹72 (b) ₹66 (c) ₹264 (d) ₹31
34. 34.If 5 kites cost ₹65, how much do 7 kites cost? (a) ₹455 (b) ₹91 (c) ₹104 (d) ₹67
35. 35.If 8 mangoes cost ₹104, how much do 9 mangoes cost? (a) ₹105 (b) ₹130 (c) ₹117 (d) ₹936
36. 36.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
37. 37.If 2 mangoes cost ₹16, how much do 10 mangoes cost? (a) ₹160 (b) ₹80 (c) ₹88 (d) ₹24
38. 38.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹40 (d) ₹45
39. 39.If 4 kites cost ₹24, how much do 6 kites cost? (a) ₹26 (b) ₹144 (c) ₹42 (d) ₹36
40. 40.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 19 days (d) 7 days

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