Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 550 · 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 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 11 days
2. 2.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹32 (c) ₹48 (d) ₹16
3. 3.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹18 (b) ₹30 (c) ₹6 (d) ₹24
4. 4.₹154 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹77 (b) ₹44 (c) ₹22 (d) ₹110
5. 5.If 2 pens cost ₹36, how much do 5 pens cost? (a) ₹108 (b) ₹39 (c) ₹180 (d) ₹90
6. 6.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹80 (b) ₹96 (c) ₹88 (d) ₹16
7. 7.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 20 days (d) 5 days
8. 8.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 4 days
9. 9.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹92 (b) ₹207 (c) ₹23 (d) ₹230
10. 10.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
11. 11.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 16 days (d) 5 days
12. 12.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹234 (b) ₹39 (c) ₹195 (d) ₹78
13. 13.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹35 (c) ₹5 (d) ₹25
14. 14.If 2 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹44 (b) ₹240 (c) ₹140 (d) ₹120
15. 15.If 7 kites cost ₹98, how much do 10 kites cost? (a) ₹140 (b) ₹101 (c) ₹154 (d) ₹980
16. 16.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 46 days (c) 17 days (d) 45 days
17. 17.If 5 notebooks cost ₹85, how much do 9 notebooks cost? (a) ₹153 (b) ₹765 (c) ₹89 (d) ₹170
18. 18.If 3 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹32 (b) ₹40 (c) ₹25 (d) ₹96
19. 19.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹370 (d) ₹333
20. 20.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 10 days (d) 8 days
21. 21.If 7 mangoes cost ₹175, how much do 2 mangoes cost? (a) ₹350 (b) ₹170 (c) ₹50 (d) ₹75
22. 22.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 17 days (d) 26 days
23. 23.If 3 kites cost ₹54, how much do 7 kites cost? (a) ₹144 (b) ₹58 (c) ₹126 (d) ₹378
24. 24.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 57 days (d) 56 days
25. 25.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 11 days (d) 8 days
26. 26.If 2 pens cost ₹10, how much do 7 pens cost? (a) ₹70 (b) ₹35 (c) ₹40 (d) ₹15
27. 27.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 11 days (d) 27 days
28. 28.If 4 kites cost ₹68, how much do 12 kites cost? (a) ₹76 (b) ₹816 (c) ₹204 (d) ₹221
29. 29.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 6 days (d) 7 days
30. 30.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹37 (b) ₹223 (c) ₹259 (d) ₹222
31. 31.If 7 kites cost ₹105, how much do 4 kites cost? (a) ₹75 (b) ₹420 (c) ₹102 (d) ₹60
32. 32.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 3 days (d) 14 days
33. 33.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹36 (d) ₹12
34. 34.If 5 kites cost ₹65, how much do 6 kites cost? (a) ₹78 (b) ₹91 (c) ₹66 (d) ₹390
35. 35.If 5 mangoes cost ₹45, how much do 11 mangoes cost? (a) ₹99 (b) ₹108 (c) ₹51 (d) ₹495
36. 36.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
37. 37.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹47 (d) ₹235
38. 38.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹81 (b) ₹36 (c) ₹90 (d) ₹9
39. 39.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹5 (c) ₹40 (d) ₹15
40. 40.If 4 mangoes cost ₹84, how much do 8 mangoes cost? (a) ₹168 (b) ₹189 (c) ₹88 (d) ₹672

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