Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 344 · 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. 1.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 52 days (c) 53 days (d) 19 days
2. 2.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹315 (b) ₹135 (c) ₹45 (d) ₹225
3. 3.If 3 notebooks cost ₹51, how much do 6 notebooks cost? (a) ₹119 (b) ₹306 (c) ₹54 (d) ₹102
4. 4.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 4 days (d) 9 days
5. 5.If 2 notebooks cost ₹44, how much do 10 notebooks cost? (a) ₹242 (b) ₹52 (c) ₹440 (d) ₹220
6. 6.If 4 pens cost ₹84, how much do 12 pens cost? (a) ₹92 (b) ₹273 (c) ₹252 (d) ₹1008
7. 7.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹240 (d) ₹220
8. 8.If 2 mangoes cost ₹50, how much do 3 mangoes cost? (a) ₹51 (b) ₹100 (c) ₹150 (d) ₹75
9. 9.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 1 day
10. 10.If 8 notebooks cost ₹120, how much do 10 notebooks cost? (a) ₹122 (b) ₹150 (c) ₹165 (d) ₹1200
11. 11.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹13 (d) ₹39
12. 12.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹18 (b) ₹108 (c) ₹126 (d) ₹90
13. 13.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹216 (b) ₹198 (c) ₹36 (d) ₹180
14. 14.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹324 (b) ₹36 (c) ₹288 (d) ₹162
15. 15.If 2 kites cost ₹8, how much do 7 kites cost? (a) ₹56 (b) ₹13 (c) ₹28 (d) ₹32
16. 16.If 2 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹88 (b) ₹132 (c) ₹66 (d) ₹45
17. 17.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 18 days (c) 8 days (d) 16 days
18. 18.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 18 days (d) 10 days
19. 19.If 5 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹122 (b) ₹192 (c) ₹168 (d) ₹840
20. 20.If 9 pens cost ₹81, how much do 5 pens cost? (a) ₹77 (b) ₹54 (c) ₹405 (d) ₹45
21. 21.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 17 days (d) 11 days
22. 22.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹132 (b) ₹45 (c) ₹66 (d) ₹88
23. 23.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 12 days (d) 13 days
24. 24.If 8 notebooks cost ₹96, how much do 3 notebooks cost? (a) ₹91 (b) ₹36 (c) ₹288 (d) ₹48
25. 25.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹10 (d) ₹35
26. 26.If 6 pens cost ₹24, how much do 7 pens cost? (a) ₹168 (b) ₹28 (c) ₹25 (d) ₹32
27. 27.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 11 days
28. 28.If 6 notebooks cost ₹66, how much do 7 notebooks cost? (a) ₹88 (b) ₹462 (c) ₹77 (d) ₹67
29. 29.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹117 (b) ₹104 (c) ₹26 (d) ₹130
30. 30.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 40 days (d) 7 days
31. 31.If 4 mangoes cost ₹36, how much do 5 mangoes cost? (a) ₹54 (b) ₹37 (c) ₹180 (d) ₹45
32. 32.If 4 pens cost ₹12, how much do 7 pens cost? (a) ₹84 (b) ₹15 (c) ₹21 (d) ₹24
33. 33.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹23 (c) ₹22 (d) ₹33
34. 34.If 3 notebooks cost ₹18, how much do 6 notebooks cost? (a) ₹36 (b) ₹42 (c) ₹108 (d) ₹21
35. 35.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹138 (d) ₹161
36. 36.₹210 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹105 (b) ₹210 (c) ₹35 (d) ₹175
37. 37.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹246 (d) ₹287
38. 38.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹108 (d) ₹126
39. 39.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 24 days (c) 7 days (d) 6 days
40. 40.If 5 mangoes cost ₹45, how much do 8 mangoes cost? (a) ₹81 (b) ₹72 (c) ₹48 (d) ₹360

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