Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 510 · 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 4 kites cost ₹100, how much do 9 kites cost? (a) ₹225 (b) ₹105 (c) ₹250 (d) ₹900
2. 2.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹248 (b) ₹279 (c) ₹31 (d) ₹155
3. 3.If 8 mangoes cost ₹56, how much do 6 mangoes cost? (a) ₹336 (b) ₹49 (c) ₹42 (d) ₹54
4. 4.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹30 (c) ₹18 (d) ₹6
5. 5.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹39 (b) ₹390 (c) ₹351 (d) ₹78
6. 6.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 19 days
7. 7.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹102 (d) ₹238
8. 8.If 7 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹39 (b) ₹24 (c) ₹30 (d) ₹168
9. 9.If 9 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹30 (b) ₹33 (c) ₹270 (d) ₹28
10. 10.If 5 pens cost ₹30, how much do 9 pens cost? (a) ₹270 (b) ₹60 (c) ₹34 (d) ₹54
11. 11.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹90 (b) ₹117 (c) ₹18 (d) ₹144
12. 12.If 3 pens cost ₹9, how much do 7 pens cost? (a) ₹63 (b) ₹13 (c) ₹24 (d) ₹21
13. 13.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 1 day
14. 14.If 7 pens cost ₹105, how much do 8 pens cost? (a) ₹135 (b) ₹840 (c) ₹120 (d) ₹106
15. 15.If 5 kites cost ₹115, how much do 4 kites cost? (a) ₹115 (b) ₹92 (c) ₹460 (d) ₹114
16. 16.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹144 (b) ₹48 (c) ₹168 (d) ₹192
17. 17.If 9 notebooks cost ₹171, how much do 11 notebooks cost? (a) ₹1881 (b) ₹173 (c) ₹209 (d) ₹228
18. 18.If 8 kites cost ₹72, how much do 10 kites cost? (a) ₹99 (b) ₹74 (c) ₹720 (d) ₹90
19. 19.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 14 days (d) 24 days
20. 20.If 2 notebooks cost ₹14, how much do 8 notebooks cost? (a) ₹112 (b) ₹56 (c) ₹20 (d) ₹63
21. 21.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 4 days (d) 27 days
22. 22.If 9 notebooks cost ₹63, how much do 10 notebooks cost? (a) ₹630 (b) ₹77 (c) ₹64 (d) ₹70
23. 23.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 4 days
24. 24.If 3 pens cost ₹69, how much do 9 pens cost? (a) ₹207 (b) ₹621 (c) ₹75 (d) ₹230
25. 25.If 9 pens cost ₹117, how much do 3 pens cost? (a) ₹52 (b) ₹351 (c) ₹111 (d) ₹39
26. 26.If 5 mangoes cost ₹45, how much do 8 mangoes cost? (a) ₹360 (b) ₹48 (c) ₹72 (d) ₹81
27. 27.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹176 (d) ₹143
28. 28.If 7 mangoes cost ₹77, how much do 9 mangoes cost? (a) ₹110 (b) ₹693 (c) ₹99 (d) ₹79
29. 29.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹111 (d) ₹74
30. 30.If 3 mangoes cost ₹66, how much do 4 mangoes cost? (a) ₹88 (b) ₹110 (c) ₹264 (d) ₹67
31. 31.If 9 pens cost ₹72, how much do 12 pens cost? (a) ₹104 (b) ₹96 (c) ₹864 (d) ₹75
32. 32.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹22 (d) ₹66
33. 33.₹352 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹220 (d) ₹176
34. 34.If 7 mangoes cost ₹126, how much do 6 mangoes cost? (a) ₹126 (b) ₹756 (c) ₹108 (d) ₹125
35. 35.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 22 days (d) 15 days
36. 36.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹26 (d) ₹13
37. 37.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹210 (b) ₹35 (c) ₹211 (d) ₹245
38. 38.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 12 days (d) 3 days
39. 39.If 2 kites cost ₹18, how much do 5 kites cost? (a) ₹45 (b) ₹54 (c) ₹90 (d) ₹21
40. 40.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹41 (d) ₹45

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