Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 4 · 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 6 kites cost ₹24, how much do 7 kites cost? (a) ₹168 (b) ₹32 (c) ₹25 (d) ₹28
2. 2.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 11 days (d) 9 days
3. 3.5 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) 5 days (d) 9 days
4. 4.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 7 days (d) 28 days
5. 5.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 10 days (d) 7 days
6. 6.If 5 notebooks cost ₹70, how much do 2 notebooks cost? (a) ₹140 (b) ₹28 (c) ₹42 (d) ₹67
7. 7.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 6 days (d) 24 days
8. 8.If 5 mangoes cost ₹110, how much do 7 mangoes cost? (a) ₹112 (b) ₹176 (c) ₹770 (d) ₹154
9. 9.₹370 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹370 (b) ₹185 (c) ₹37 (d) ₹333
10. 10.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 10 days (d) 16 days
11. 11.If 8 notebooks cost ₹88, how much do 2 notebooks cost? (a) ₹176 (b) ₹82 (c) ₹33 (d) ₹22
12. 12.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹105 (d) ₹140
13. 13.If 8 pens cost ₹112, how much do 10 pens cost? (a) ₹114 (b) ₹140 (c) ₹154 (d) ₹1120
14. 14.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹124 (d) ₹186
15. 15.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹66 (b) ₹77 (c) ₹55 (d) ₹11
16. 16.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 4 days (d) 5 days
17. 17.If 5 kites cost ₹25, how much do 6 kites cost? (a) ₹26 (b) ₹35 (c) ₹150 (d) ₹30
18. 18.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹70 (c) ₹210 (d) ₹35
19. 19.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
20. 20.₹374 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹102 (b) ₹187 (c) ₹34 (d) ₹272
21. 21.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹51 (b) ₹153 (c) ₹136 (d) ₹17
22. 22.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 13 days (d) 9 days
23. 23.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹300 (b) ₹50 (c) ₹150 (d) ₹250
24. 24.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 28 days (d) 29 days
25. 25.If 5 kites cost ₹110, how much do 8 kites cost? (a) ₹880 (b) ₹198 (c) ₹176 (d) ₹113
26. 26.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹288 (d) ₹324
27. 27.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 5 days
28. 28.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹60 (d) ₹90
29. 29.If 3 kites cost ₹45, how much do 4 kites cost? (a) ₹180 (b) ₹60 (c) ₹46 (d) ₹75
30. 30.If 8 pens cost ₹120, how much do 5 pens cost? (a) ₹75 (b) ₹117 (c) ₹600 (d) ₹90
31. 31.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 13 days (d) 9 days
32. 32.If 7 notebooks cost ₹35, how much do 5 notebooks cost? (a) ₹30 (b) ₹175 (c) ₹33 (d) ₹25
33. 33.₹171 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹19 (b) ₹153 (c) ₹171 (d) ₹152
34. 34.If 2 kites cost ₹42, how much do 6 kites cost? (a) ₹46 (b) ₹252 (c) ₹126 (d) ₹147
35. 35.If 8 pens cost ₹160, how much do 12 pens cost? (a) ₹260 (b) ₹240 (c) ₹1920 (d) ₹164
36. 36.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 3 days (d) 46 days
37. 37.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹120 (d) ₹280
38. 38.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹200 (b) ₹325 (c) ₹50 (d) ₹450
39. 39.₹234 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹52 (b) ₹117 (c) ₹26 (d) ₹182
40. 40.If 9 kites cost ₹63, how much do 7 kites cost? (a) ₹61 (b) ₹441 (c) ₹56 (d) ₹49

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