Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 964 · 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.If 2 notebooks cost ₹20, how much do 10 notebooks cost? (a) ₹200 (b) ₹110 (c) ₹100 (d) ₹28
2. 2.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 4 days (d) 3 days
3. 3.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
4. 4.If 2 mangoes cost ₹18, how much do 10 mangoes cost? (a) ₹26 (b) ₹180 (c) ₹99 (d) ₹90
5. 5.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
6. 6.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 5 days (d) 7 days
7. 7.If 7 notebooks cost ₹105, how much do 8 notebooks cost? (a) ₹120 (b) ₹106 (c) ₹840 (d) ₹135
8. 8.If 4 pens cost ₹24, how much do 3 pens cost? (a) ₹72 (b) ₹18 (c) ₹23 (d) ₹24
9. 9.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹11 (b) ₹45 (c) ₹44 (d) ₹55
10. 10.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 6 days
11. 11.If 2 pens cost ₹34, how much do 8 pens cost? (a) ₹40 (b) ₹153 (c) ₹136 (d) ₹272
12. 12.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹182 (b) ₹104 (c) ₹26 (d) ₹208
13. 13.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 1 day (d) 11 days
14. 14.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 5 days (d) 4 days
15. 15.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹33 (b) ₹77 (c) ₹55 (d) ₹11
16. 16.If 3 mangoes cost ₹69, how much do 4 mangoes cost? (a) ₹115 (b) ₹276 (c) ₹70 (d) ₹92
17. 17.If 3 mangoes cost ₹33, how much do 5 mangoes cost? (a) ₹165 (b) ₹66 (c) ₹55 (d) ₹35
18. 18.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 9 days (d) 15 days
19. 19.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 3 days (d) 4 days
20. 20.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
21. 21.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹230 (b) ₹23 (c) ₹207 (d) ₹92
22. 22.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 8 days (d) 7 days
23. 23.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹80 (d) ₹48
24. 24.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹62 (b) ₹186 (c) ₹155 (d) ₹31
25. 25.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹24 (d) ₹42
26. 26.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹306 (b) ₹187 (c) ₹34 (d) ₹68
27. 27.If 4 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹420 (b) ₹105 (c) ₹85 (d) ₹126
28. 28.If 9 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹154 (b) ₹127 (c) ₹1260 (d) ₹140
29. 29.If 4 notebooks cost ₹68, how much do 5 notebooks cost? (a) ₹340 (b) ₹69 (c) ₹85 (d) ₹102
30. 30.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 7 days
31. 31.₹168 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹168 (c) ₹24 (d) ₹144
32. 32.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹343 (b) ₹147 (c) ₹245 (d) ₹49
33. 33.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 1 day
34. 34.₹152 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹95 (b) ₹76 (c) ₹57 (d) ₹19
35. 35.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 2 days (d) 1 day
36. 36.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 6 days (d) 5 days
37. 37.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 4 days (d) 5 days
38. 38.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹80 (b) ₹60 (c) ₹20 (d) ₹70
39. 39.If 9 kites cost ₹45, how much do 11 kites cost? (a) ₹60 (b) ₹495 (c) ₹47 (d) ₹55
40. 40.If 7 kites cost ₹105, how much do 10 kites cost? (a) ₹165 (b) ₹1050 (c) ₹150 (d) ₹108

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