Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 635 · 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.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹45 (d) ₹25
2. 2.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹80 (b) ₹100 (c) ₹240 (d) ₹61
3. 3.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 14 days (d) 12 days
4. 4.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 6 days (c) 14 days (d) 30 days
5. 5.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 37 days (d) 3 days
6. 6.If 8 pens cost ₹128, how much do 4 pens cost? (a) ₹512 (b) ₹80 (c) ₹64 (d) ₹124
7. 7.If 8 kites cost ₹120, how much do 2 kites cost? (a) ₹240 (b) ₹45 (c) ₹114 (d) ₹30
8. 8.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹52 (d) ₹39
9. 9.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹51 (d) ₹85
10. 10.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹155 (b) ₹93 (c) ₹31 (d) ₹217
11. 11.If 5 pens cost ₹20, how much do 7 pens cost? (a) ₹140 (b) ₹32 (c) ₹28 (d) ₹22
12. 12.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹138 (b) ₹23 (c) ₹161 (d) ₹139
13. 13.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹198 (b) ₹177 (c) ₹220 (d) ₹1584
14. 14.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹84 (b) ₹105 (c) ₹21 (d) ₹126
15. 15.If 7 pens cost ₹105, how much do 3 pens cost? (a) ₹60 (b) ₹101 (c) ₹315 (d) ₹45
16. 16.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹207 (b) ₹184 (c) ₹23 (d) ₹115
17. 17.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹162 (b) ₹18 (c) ₹180 (d) ₹90
18. 18.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹128 (b) ₹112 (c) ₹64 (d) ₹16
19. 19.If 7 mangoes cost ₹49, how much do 2 mangoes cost? (a) ₹14 (b) ₹44 (c) ₹98 (d) ₹21
20. 20.If 4 notebooks cost ₹52, how much do 6 notebooks cost? (a) ₹91 (b) ₹312 (c) ₹78 (d) ₹54
21. 21.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹160 (d) ₹80
22. 22.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 24 days (d) 14 days
23. 23.If 8 notebooks cost ₹88, how much do 10 notebooks cost? (a) ₹880 (b) ₹121 (c) ₹90 (d) ₹110
24. 24.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 56 days (b) 20 days (c) 57 days (d) 8 days
25. 25.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 3 days (d) 11 days
26. 26.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹66 (b) ₹11 (c) ₹44 (d) ₹55
27. 27.If 2 notebooks cost ₹22, how much do 7 notebooks cost? (a) ₹27 (b) ₹77 (c) ₹88 (d) ₹154
28. 28.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 13 days (d) 17 days
29. 29.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹60 (b) ₹45 (c) ₹15 (d) ₹75
30. 30.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 9 days (d) 3 days
31. 31.If 9 mangoes cost ₹162, how much do 11 mangoes cost? (a) ₹198 (b) ₹164 (c) ₹216 (d) ₹1782
32. 32.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 7 days
33. 33.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹26 (b) ₹182 (c) ₹208 (d) ₹104
34. 34.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 17 days (d) 10 days
35. 35.If 7 notebooks cost ₹63, how much do 8 notebooks cost? (a) ₹72 (b) ₹81 (c) ₹64 (d) ₹504
36. 36.₹240 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹40 (b) ₹120 (c) ₹240 (d) ₹200
37. 37.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 4 days
38. 38.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 45 days (d) 21 days
39. 39.If 3 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹22 (b) ₹126 (c) ₹42 (d) ₹48
40. 40.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 8 days (d) 9 days

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