Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 309 · 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.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹5 (b) ₹45 (c) ₹10 (d) ₹50
2. 2.If 3 pens cost ₹69, how much do 8 pens cost? (a) ₹552 (b) ₹184 (c) ₹207 (d) ₹74
3. 3.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹20 (c) ₹100 (d) ₹140
4. 4.If 9 notebooks cost ₹162, how much do 12 notebooks cost? (a) ₹1944 (b) ₹216 (c) ₹165 (d) ₹234
5. 5.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹99 (b) ₹132 (c) ₹165 (d) ₹33
6. 6.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 2 days (d) 10 days
7. 7.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 21 days (d) 22 days
8. 8.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹273 (b) ₹312 (c) ₹39 (d) ₹156
9. 9.If 7 notebooks cost ₹112, how much do 9 notebooks cost? (a) ₹1008 (b) ₹144 (c) ₹160 (d) ₹114
10. 10.If 7 kites cost ₹98, how much do 6 kites cost? (a) ₹84 (b) ₹98 (c) ₹588 (d) ₹97
11. 11.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹117 (b) ₹65 (c) ₹13 (d) ₹130
12. 12.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹136 (b) ₹34 (c) ₹119 (d) ₹17
13. 13.If 3 mangoes cost ₹57, how much do 4 mangoes cost? (a) ₹228 (b) ₹58 (c) ₹95 (d) ₹76
14. 14.If 2 notebooks cost ₹44, how much do 4 notebooks cost? (a) ₹176 (b) ₹88 (c) ₹110 (d) ₹46
15. 15.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹162 (d) ₹189
16. 16.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 8 days (d) 9 days
17. 17.If 6 pens cost ₹102, how much do 2 pens cost? (a) ₹204 (b) ₹98 (c) ₹34 (d) ₹51
18. 18.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 20 days (d) 21 days
19. 19.If 7 kites cost ₹140, how much do 9 kites cost? (a) ₹1260 (b) ₹200 (c) ₹180 (d) ₹142
20. 20.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹24 (b) ₹42 (c) ₹60 (d) ₹12
21. 21.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 19 days (d) 9 days
22. 22.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹87 (d) ₹116
23. 23.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹336 (b) ₹240 (c) ₹432 (d) ₹48
24. 24.If 8 pens cost ₹184, how much do 6 pens cost? (a) ₹138 (b) ₹1104 (c) ₹161 (d) ₹182
25. 25.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
26. 26.₹49 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹42 (b) ₹7 (c) ₹49 (d) ₹43
27. 27.If 6 pens cost ₹48, how much do 10 pens cost? (a) ₹52 (b) ₹80 (c) ₹480 (d) ₹88
28. 28.If 9 kites cost ₹63, how much do 12 kites cost? (a) ₹84 (b) ₹66 (c) ₹756 (d) ₹91
29. 29.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 6 days (d) 4 days
30. 30.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 16 days (d) 12 days
31. 31.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 9 days
32. 32.If 4 kites cost ₹48, how much do 6 kites cost? (a) ₹84 (b) ₹72 (c) ₹50 (d) ₹288
33. 33.If 7 pens cost ₹112, how much do 11 pens cost? (a) ₹116 (b) ₹1232 (c) ₹176 (d) ₹192
34. 34.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹17 (d) ₹102
35. 35.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹25 (b) ₹30 (c) ₹35 (d) ₹5
36. 36.If 3 notebooks cost ₹69, how much do 5 notebooks cost? (a) ₹71 (b) ₹138 (c) ₹345 (d) ₹115
37. 37.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 9 days (d) 13 days
38. 38.If 5 pens cost ₹80, how much do 2 pens cost? (a) ₹160 (b) ₹77 (c) ₹48 (d) ₹32
39. 39.If 3 mangoes cost ₹51, how much do 9 mangoes cost? (a) ₹170 (b) ₹153 (c) ₹459 (d) ₹57
40. 40.If 6 kites cost ₹102, how much do 4 kites cost? (a) ₹85 (b) ₹100 (c) ₹408 (d) ₹68

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