Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 438 · 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.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹184 (b) ₹92 (c) ₹46 (d) ₹138
2. 2.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 15 days (d) 5 days
3. 3.If 6 pens cost ₹102, how much do 12 pens cost? (a) ₹108 (b) ₹204 (c) ₹1224 (d) ₹221
4. 4.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 32 days (c) 17 days (d) 33 days
5. 5.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹24 (b) ₹60 (c) ₹96 (d) ₹120
6. 6.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 19 days (c) 11 days (d) 35 days
7. 7.If 7 pens cost ₹105, how much do 6 pens cost? (a) ₹90 (b) ₹105 (c) ₹630 (d) ₹104
8. 8.If 6 pens cost ₹18, how much do 7 pens cost? (a) ₹24 (b) ₹126 (c) ₹21 (d) ₹19
9. 9.If 8 kites cost ₹64, how much do 6 kites cost? (a) ₹62 (b) ₹48 (c) ₹384 (d) ₹56
10. 10.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 4 days (d) 3 days
11. 11.If 9 kites cost ₹144, how much do 3 kites cost? (a) ₹432 (b) ₹138 (c) ₹48 (d) ₹64
12. 12.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹36 (d) ₹54
13. 13.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹52 (b) ₹130 (c) ₹13 (d) ₹117
14. 14.If 5 notebooks cost ₹35, how much do 6 notebooks cost? (a) ₹49 (b) ₹36 (c) ₹42 (d) ₹210
15. 15.If 3 pens cost ₹66, how much do 10 pens cost? (a) ₹73 (b) ₹660 (c) ₹242 (d) ₹220
16. 16.If 2 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹60 (b) ₹36 (c) ₹15 (d) ₹30
17. 17.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹410 (b) ₹41 (c) ₹205 (d) ₹369
18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
19. 19.If 6 pens cost ₹18, how much do 3 pens cost? (a) ₹12 (b) ₹9 (c) ₹15 (d) ₹54
20. 20.If 2 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹60 (b) ₹15 (c) ₹36 (d) ₹30
21. 21.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹35 (d) ₹25
22. 22.If 2 notebooks cost ₹34, how much do 4 notebooks cost? (a) ₹136 (b) ₹68 (c) ₹85 (d) ₹36
23. 23.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹250 (d) ₹450
24. 24.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 10 days (c) 40 days (d) 41 days
25. 25.If 2 mangoes cost ₹20, how much do 5 mangoes cost? (a) ₹60 (b) ₹23 (c) ₹50 (d) ₹100
26. 26.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 7 days
27. 27.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹8 (d) ₹20
28. 28.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹74 (b) ₹37 (c) ₹333 (d) ₹370
29. 29.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹192 (b) ₹120 (c) ₹24 (d) ₹156
30. 30.If 5 notebooks cost ₹60, how much do 12 notebooks cost? (a) ₹720 (b) ₹144 (c) ₹67 (d) ₹156
31. 31.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹25 (c) ₹20 (d) ₹5
32. 32.If 4 kites cost ₹92, how much do 7 kites cost? (a) ₹161 (b) ₹644 (c) ₹184 (d) ₹95
33. 33.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 7 days
34. 34.If 6 notebooks cost ₹132, how much do 12 notebooks cost? (a) ₹1584 (b) ₹286 (c) ₹138 (d) ₹264
35. 35.If 4 pens cost ₹52, how much do 10 pens cost? (a) ₹520 (b) ₹143 (c) ₹130 (d) ₹58
36. 36.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹108 (b) ₹243 (c) ₹27 (d) ₹270
37. 37.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 6 days (d) 7 days
38. 38.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 11 days (d) 15 days
39. 39.If 7 kites cost ₹56, how much do 6 kites cost? (a) ₹336 (b) ₹56 (c) ₹48 (d) ₹55
40. 40.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹80 (b) ₹96 (c) ₹88 (d) ₹16

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