Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 285 · 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.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹176 (c) ₹220 (d) ₹44
2. 2.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹221 (b) ₹306 (c) ₹136 (d) ₹34
3. 3.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹45 (b) ₹9 (c) ₹63 (d) ₹54
4. 4.If 7 kites cost ₹119, how much do 12 kites cost? (a) ₹204 (b) ₹1428 (c) ₹221 (d) ₹124
5. 5.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹240 (b) ₹192 (c) ₹120 (d) ₹48
6. 6.If 4 notebooks cost ₹88, how much do 3 notebooks cost? (a) ₹264 (b) ₹87 (c) ₹66 (d) ₹88
7. 7.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹92 (b) ₹69 (c) ₹23 (d) ₹115
8. 8.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹20 (b) ₹13 (c) ₹48 (d) ₹16
9. 9.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹22 (b) ₹132 (c) ₹66 (d) ₹110
10. 10.If 6 kites cost ₹36, how much do 4 kites cost? (a) ₹30 (b) ₹24 (c) ₹144 (d) ₹34
11. 11.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 48 days (c) 18 days (d) 6 days
12. 12.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹18 (c) ₹21 (d) ₹6
13. 13.If 3 kites cost ₹48, how much do 12 kites cost? (a) ₹208 (b) ₹192 (c) ₹576 (d) ₹57
14. 14.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹264 (b) ₹297 (c) ₹33 (d) ₹165
15. 15.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹209 (b) ₹38 (c) ₹190 (d) ₹228
16. 16.If 5 pens cost ₹40, how much do 3 pens cost? (a) ₹38 (b) ₹120 (c) ₹32 (d) ₹24
17. 17.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹10 (b) ₹25 (c) ₹50 (d) ₹40
18. 18.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 5 days
19. 19.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹70 (c) ₹10 (d) ₹60
20. 20.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹75 (b) ₹100 (c) ₹25 (d) ₹125
21. 21.If 8 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹12 (b) ₹42 (c) ₹96 (d) ₹18
22. 22.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹378 (b) ₹336 (c) ₹189 (d) ₹42
23. 23.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹22 (b) ₹198 (c) ₹154 (d) ₹110
24. 24.If 9 pens cost ₹117, how much do 5 pens cost? (a) ₹65 (b) ₹113 (c) ₹585 (d) ₹78
25. 25.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹150 (b) ₹25 (c) ₹125 (d) ₹100
26. 26.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹175 (c) ₹210 (d) ₹35
27. 27.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 16 days (d) 10 days
28. 28.If 4 notebooks cost ₹28, how much do 8 notebooks cost? (a) ₹224 (b) ₹32 (c) ₹63 (d) ₹56
29. 29.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 1 day (d) 3 days
30. 30.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹12 (d) ₹72
31. 31.If 8 kites cost ₹104, how much do 5 kites cost? (a) ₹78 (b) ₹101 (c) ₹520 (d) ₹65
32. 32.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 40 days (c) 16 days (d) 41 days
33. 33.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 3 days (d) 9 days
34. 34.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 18 days (c) 15 days (d) 8 days
35. 35.If 5 notebooks cost ₹65, how much do 4 notebooks cost? (a) ₹260 (b) ₹52 (c) ₹64 (d) ₹65
36. 36.If 9 kites cost ₹45, how much do 5 kites cost? (a) ₹30 (b) ₹41 (c) ₹25 (d) ₹225
37. 37.If 9 mangoes cost ₹225, how much do 4 mangoes cost? (a) ₹900 (b) ₹220 (c) ₹100 (d) ₹125
38. 38.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 13 days (d) 12 days
39. 39.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹156 (b) ₹195 (c) ₹234 (d) ₹39
40. 40.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹13 (b) ₹36 (c) ₹18 (d) ₹24

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