Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 502 · 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. 1.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 11 days (d) 13 days
2. 2.If 3 pens cost ₹75, how much do 6 pens cost? (a) ₹150 (b) ₹450 (c) ₹175 (d) ₹78
3. 3.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 17 days (c) 5 days (d) 45 days
4. 4.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹108 (b) ₹126 (c) ₹90 (d) ₹18
5. 5.If 8 notebooks cost ₹160, how much do 9 notebooks cost? (a) ₹161 (b) ₹180 (c) ₹1440 (d) ₹200
6. 6.If 2 pens cost ₹26, how much do 3 pens cost? (a) ₹39 (b) ₹52 (c) ₹78 (d) ₹27
7. 7.If 6 kites cost ₹30, how much do 8 kites cost? (a) ₹240 (b) ₹40 (c) ₹45 (d) ₹32
8. 8.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 27 days (d) 15 days
9. 9.₹360 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹80 (b) ₹280 (c) ₹40 (d) ₹180
10. 10.If 6 pens cost ₹108, how much do 4 pens cost? (a) ₹106 (b) ₹72 (c) ₹90 (d) ₹432
11. 11.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹135 (b) ₹81 (c) ₹108 (d) ₹27
12. 12.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹35 (c) ₹42 (d) ₹28
13. 13.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 3 days
14. 14.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹144 (b) ₹16 (c) ₹32 (d) ₹88
15. 15.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹336 (b) ₹231 (c) ₹42 (d) ₹126
16. 16.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 16 days (d) 17 days
17. 17.5 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
18. 18.If 9 mangoes cost ₹27, how much do 6 mangoes cost? (a) ₹21 (b) ₹18 (c) ₹24 (d) ₹162
19. 19.If 3 pens cost ₹48, how much do 5 pens cost? (a) ₹240 (b) ₹80 (c) ₹50 (d) ₹96
20. 20.If 3 pens cost ₹12, how much do 7 pens cost? (a) ₹28 (b) ₹16 (c) ₹32 (d) ₹84
21. 21.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹39 (d) ₹78
22. 22.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 10 days (d) 8 days
23. 23.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹392 (b) ₹49 (c) ₹147 (d) ₹441
24. 24.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 5 days (d) 4 days
25. 25.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹180 (d) ₹108
26. 26.If 9 pens cost ₹90, how much do 2 pens cost? (a) ₹30 (b) ₹20 (c) ₹83 (d) ₹180
27. 27.If 3 kites cost ₹9, how much do 9 kites cost? (a) ₹81 (b) ₹27 (c) ₹30 (d) ₹15
28. 28.If 8 mangoes cost ₹64, how much do 4 mangoes cost? (a) ₹256 (b) ₹60 (c) ₹40 (d) ₹32
29. 29.If 5 pens cost ₹20, how much do 7 pens cost? (a) ₹22 (b) ₹140 (c) ₹28 (d) ₹32
30. 30.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹72 (d) ₹60
31. 31.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹88 (d) ₹96
32. 32.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹10 (b) ₹90 (c) ₹100 (d) ₹50
33. 33.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹132 (b) ₹96 (c) ₹24 (d) ₹168
34. 34.If 9 notebooks cost ₹135, how much do 7 notebooks cost? (a) ₹133 (b) ₹120 (c) ₹945 (d) ₹105
35. 35.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹300 (c) ₹275 (d) ₹250
36. 36.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹39 (b) ₹273 (c) ₹235 (d) ₹234
37. 37.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 16 days (d) 11 days
38. 38.If 2 pens cost ₹36, how much do 3 pens cost? (a) ₹37 (b) ₹72 (c) ₹108 (d) ₹54
39. 39.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹161 (d) ₹138
40. 40.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 1 day (d) 27 days

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