Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 658 · 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 7 kites cost ₹42, how much do 9 kites cost? (a) ₹54 (b) ₹378 (c) ₹44 (d) ₹60
2. 2.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹18 (d) ₹21
3. 3.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹85 (d) ₹68
4. 4.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹68 (d) ₹17
5. 5.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 22 days (d) 21 days
6. 6.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹136 (c) ₹17 (d) ₹153
7. 7.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 6 days (d) 36 days
8. 8.If 7 mangoes cost ₹133, how much do 5 mangoes cost? (a) ₹114 (b) ₹665 (c) ₹131 (d) ₹95
9. 9.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹63 (b) ₹62 (c) ₹31 (d) ₹93
10. 10.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹11 (d) ₹77
11. 11.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹72 (c) ₹16 (d) ₹128
12. 12.If 8 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹51 (b) ₹28 (c) ₹168 (d) ₹21
13. 13.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹248 (d) ₹217
14. 14.If 4 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹99 (b) ₹396 (c) ₹43 (d) ₹108
15. 15.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 3 days (d) 7 days
16. 16.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹162 (d) ₹126
17. 17.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 9 days (d) 10 days
18. 18.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 17 days (d) 13 days
19. 19.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 28 days (d) 3 days
20. 20.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹105 (b) ₹126 (c) ₹147 (d) ₹21
21. 21.If 7 mangoes cost ₹126, how much do 8 mangoes cost? (a) ₹1008 (b) ₹127 (c) ₹144 (d) ₹162
22. 22.If 3 notebooks cost ₹66, how much do 6 notebooks cost? (a) ₹132 (b) ₹154 (c) ₹396 (d) ₹69
23. 23.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹80 (d) ₹72
24. 24.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹95 (b) ₹114 (c) ₹19 (d) ₹133
25. 25.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹387 (b) ₹345 (c) ₹344 (d) ₹43
26. 26.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹90 (b) ₹210 (c) ₹30 (d) ₹150
27. 27.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹65 (d) ₹78
28. 28.If 9 pens cost ₹216, how much do 10 pens cost? (a) ₹2160 (b) ₹264 (c) ₹240 (d) ₹217
29. 29.If 2 notebooks cost ₹38, how much do 9 notebooks cost? (a) ₹45 (b) ₹342 (c) ₹190 (d) ₹171
30. 30.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 13 days (d) 12 days
31. 31.If 2 pens cost ₹32, how much do 9 pens cost? (a) ₹39 (b) ₹160 (c) ₹288 (d) ₹144
32. 32.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 17 days
33. 33.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹300 (b) ₹350 (c) ₹50 (d) ₹250
34. 34.If 9 notebooks cost ₹54, how much do 11 notebooks cost? (a) ₹66 (b) ₹56 (c) ₹594 (d) ₹72
35. 35.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 11 days
36. 36.If 5 notebooks cost ₹15, how much do 2 notebooks cost? (a) ₹12 (b) ₹6 (c) ₹30 (d) ₹9
37. 37.If 9 notebooks cost ₹225, how much do 2 notebooks cost? (a) ₹75 (b) ₹50 (c) ₹218 (d) ₹450
38. 38.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹35 (c) ₹7 (d) ₹28
39. 39.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹18 (b) ₹6 (c) ₹30 (d) ₹24
40. 40.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 16 days (d) 1 day

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