Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 7 · 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 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 2 days (d) 1 day
2. 2.If 4 notebooks cost ₹40, how much do 2 notebooks cost? (a) ₹30 (b) ₹80 (c) ₹38 (d) ₹20
3. 3.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹35 (b) ₹14 (c) ₹28 (d) ₹42
4. 4.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 7 days (d) 4 days
5. 5.If 9 pens cost ₹171, how much do 10 pens cost? (a) ₹209 (b) ₹1710 (c) ₹190 (d) ₹172
6. 6.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹49 (b) ₹56 (c) ₹28 (d) ₹7
7. 7.₹133 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹57 (b) ₹95 (c) ₹19 (d) ₹76
8. 8.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 1 day (d) 11 days
9. 9.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹30 (b) ₹39 (c) ₹48 (d) ₹6
10. 10.If 6 kites cost ₹138, how much do 7 kites cost? (a) ₹139 (b) ₹966 (c) ₹184 (d) ₹161
11. 11.If 2 pens cost ₹8, how much do 9 pens cost? (a) ₹36 (b) ₹15 (c) ₹40 (d) ₹72
12. 12.If 2 pens cost ₹18, how much do 12 pens cost? (a) ₹108 (b) ₹117 (c) ₹28 (d) ₹216
13. 13.₹432 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹384 (b) ₹216 (c) ₹48 (d) ₹432
14. 14.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 21 days (c) 10 days (d) 20 days
15. 15.If 3 kites cost ₹72, how much do 2 kites cost? (a) ₹71 (b) ₹144 (c) ₹72 (d) ₹48
16. 16.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹96 (c) ₹48 (d) ₹24
17. 17.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 5 days (d) 45 days
18. 18.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 16 days (d) 9 days
19. 19.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹17 (b) ₹51 (c) ₹34 (d) ₹68
20. 20.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹32 (b) ₹64 (c) ₹144 (d) ₹224
21. 21.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹160 (d) ₹288
22. 22.If 2 kites cost ₹42, how much do 4 kites cost? (a) ₹168 (b) ₹44 (c) ₹105 (d) ₹84
23. 23.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 19 days (d) 18 days
24. 24.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹87 (b) ₹116 (c) ₹145 (d) ₹29
25. 25.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 5 days (d) 6 days
26. 26.If 7 mangoes cost ₹133, how much do 3 mangoes cost? (a) ₹399 (b) ₹129 (c) ₹57 (d) ₹76
27. 27.₹320 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹160 (d) ₹200
28. 28.If 7 kites cost ₹154, how much do 11 kites cost? (a) ₹242 (b) ₹264 (c) ₹1694 (d) ₹158
29. 29.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹36 (b) ₹45 (c) ₹37 (d) ₹9
30. 30.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 17 days (d) 44 days
31. 31.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹20 (c) ₹100 (d) ₹140
32. 32.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 7 days (d) 4 days
33. 33.If 9 pens cost ₹207, how much do 3 pens cost? (a) ₹621 (b) ₹69 (c) ₹201 (d) ₹92
34. 34.If 8 pens cost ₹40, how much do 10 pens cost? (a) ₹400 (b) ₹42 (c) ₹55 (d) ₹50
35. 35.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹6 (c) ₹15 (d) ₹12
36. 36.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹121 (b) ₹120 (c) ₹135 (d) ₹15
37. 37.₹343 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹98 (b) ₹49 (c) ₹294 (d) ₹245
38. 38.If 8 pens cost ₹32, how much do 9 pens cost? (a) ₹40 (b) ₹288 (c) ₹36 (d) ₹33
39. 39.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹6 (c) ₹27 (d) ₹12
40. 40.If 2 mangoes cost ₹34, how much do 11 mangoes cost? (a) ₹204 (b) ₹187 (c) ₹374 (d) ₹43

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