Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 733 · 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. 1.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 7 days (c) 33 days (d) 15 days
2. 2.If 9 kites cost ₹45, how much do 5 kites cost? (a) ₹41 (b) ₹25 (c) ₹225 (d) ₹30
3. 3.If 3 notebooks cost ₹63, how much do 6 notebooks cost? (a) ₹66 (b) ₹378 (c) ₹147 (d) ₹126
4. 4.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹45 (b) ₹225 (c) ₹135 (d) ₹180
5. 5.If 3 pens cost ₹33, how much do 2 pens cost? (a) ₹33 (b) ₹66 (c) ₹22 (d) ₹32
6. 6.If 4 notebooks cost ₹92, how much do 7 notebooks cost? (a) ₹644 (b) ₹161 (c) ₹95 (d) ₹184
7. 7.If 8 kites cost ₹184, how much do 4 kites cost? (a) ₹736 (b) ₹92 (c) ₹180 (d) ₹115
8. 8.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 10 days (d) 4 days
9. 9.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 44 days (c) 5 days (d) 45 days
10. 10.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 6 days
11. 11.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹63 (c) ₹126 (d) ₹84
12. 12.₹550 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹450 (b) ₹100 (c) ₹275 (d) ₹50
13. 13.If 3 mangoes cost ₹75, how much do 5 mangoes cost? (a) ₹125 (b) ₹77 (c) ₹375 (d) ₹150
14. 14.If 2 kites cost ₹6, how much do 9 kites cost? (a) ₹54 (b) ₹30 (c) ₹13 (d) ₹27
15. 15.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹10 (c) ₹20 (d) ₹5
16. 16.If 7 notebooks cost ₹168, how much do 8 notebooks cost? (a) ₹169 (b) ₹192 (c) ₹1344 (d) ₹216
17. 17.If 5 pens cost ₹70, how much do 6 pens cost? (a) ₹71 (b) ₹98 (c) ₹84 (d) ₹420
18. 18.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹10 (b) ₹90 (c) ₹20 (d) ₹55
19. 19.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹11 (b) ₹99 (c) ₹55 (d) ₹110
20. 20.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 7 days
21. 21.If 7 kites cost ₹161, how much do 8 kites cost? (a) ₹162 (b) ₹207 (c) ₹184 (d) ₹1288
22. 22.If 2 mangoes cost ₹18, how much do 10 mangoes cost? (a) ₹99 (b) ₹90 (c) ₹180 (d) ₹26
23. 23.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹32 (b) ₹256 (c) ₹128 (d) ₹224
24. 24.If 9 mangoes cost ₹99, how much do 12 mangoes cost? (a) ₹102 (b) ₹1188 (c) ₹143 (d) ₹132
25. 25.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 1 day (d) 17 days
26. 26.₹72 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹72 (d) ₹63
27. 27.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
28. 28.If 4 kites cost ₹28, how much do 9 kites cost? (a) ₹252 (b) ₹33 (c) ₹70 (d) ₹63
29. 29.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 2 days (d) 12 days
30. 30.If 5 kites cost ₹15, how much do 8 kites cost? (a) ₹120 (b) ₹27 (c) ₹24 (d) ₹18
31. 31.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹126 (d) ₹147
32. 32.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹48 (d) ₹36
33. 33.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 56 days (b) 57 days (c) 8 days (d) 20 days
34. 34.If 9 pens cost ₹45, how much do 2 pens cost? (a) ₹90 (b) ₹10 (c) ₹15 (d) ₹38
35. 35.If 3 pens cost ₹18, how much do 9 pens cost? (a) ₹24 (b) ₹54 (c) ₹60 (d) ₹162
36. 36.If 3 kites cost ₹48, how much do 12 kites cost? (a) ₹57 (b) ₹208 (c) ₹576 (d) ₹192
37. 37.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹240 (b) ₹120 (c) ₹192 (d) ₹48
38. 38.5 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) 4 days (d) 6 days
39. 39.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 36 days (c) 35 days (d) 11 days
40. 40.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹8 (b) ₹72 (c) ₹40 (d) ₹80

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