Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 772 · 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.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹110 (c) ₹22 (d) ₹66
2. 2.If 6 notebooks cost ₹90, how much do 5 notebooks cost? (a) ₹89 (b) ₹450 (c) ₹90 (d) ₹75
3. 3.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 2 days
4. 4.If 2 notebooks cost ₹18, how much do 10 notebooks cost? (a) ₹99 (b) ₹90 (c) ₹26 (d) ₹180
5. 5.If 2 pens cost ₹8, how much do 10 pens cost? (a) ₹44 (b) ₹16 (c) ₹80 (d) ₹40
6. 6.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
7. 7.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹192 (b) ₹176 (c) ₹32 (d) ₹160
8. 8.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹95 (b) ₹133 (c) ₹171 (d) ₹19
9. 9.If 8 pens cost ₹32, how much do 10 pens cost? (a) ₹40 (b) ₹44 (c) ₹320 (d) ₹34
10. 10.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 9 days (d) 8 days
11. 11.If 4 pens cost ₹96, how much do 5 pens cost? (a) ₹144 (b) ₹120 (c) ₹480 (d) ₹97
12. 12.₹190 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹95 (b) ₹19 (c) ₹133 (d) ₹57
13. 13.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹115 (d) ₹23
14. 14.₹92 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹23 (d) ₹69
15. 15.If 9 pens cost ₹108, how much do 5 pens cost? (a) ₹104 (b) ₹72 (c) ₹540 (d) ₹60
16. 16.If 2 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹52 (b) ₹273 (c) ₹504 (d) ₹252
17. 17.If 7 kites cost ₹84, how much do 6 kites cost? (a) ₹83 (b) ₹504 (c) ₹84 (d) ₹72
18. 18.If 6 pens cost ₹126, how much do 5 pens cost? (a) ₹105 (b) ₹126 (c) ₹125 (d) ₹630
19. 19.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹50 (b) ₹325 (c) ₹200 (d) ₹450
20. 20.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹18 (d) ₹126
21. 21.If 8 mangoes cost ₹80, how much do 12 mangoes cost? (a) ₹84 (b) ₹120 (c) ₹960 (d) ₹130
22. 22.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹45 (c) ₹40 (d) ₹5
23. 23.If 9 notebooks cost ₹108, how much do 5 notebooks cost? (a) ₹72 (b) ₹540 (c) ₹104 (d) ₹60
24. 24.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹280 (b) ₹220 (c) ₹160 (d) ₹40
25. 25.If 5 mangoes cost ₹90, how much do 3 mangoes cost? (a) ₹72 (b) ₹270 (c) ₹88 (d) ₹54
26. 26.If 2 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹144 (b) ₹51 (c) ₹120 (d) ₹240
27. 27.If 2 notebooks cost ₹14, how much do 3 notebooks cost? (a) ₹42 (b) ₹28 (c) ₹21 (d) ₹15
28. 28.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 4 days (d) 5 days
29. 29.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹392 (b) ₹441 (c) ₹49 (d) ₹245
30. 30.If 8 kites cost ₹128, how much do 12 kites cost? (a) ₹192 (b) ₹132 (c) ₹208 (d) ₹1536
31. 31.If 9 pens cost ₹225, how much do 3 pens cost? (a) ₹100 (b) ₹219 (c) ₹675 (d) ₹75
32. 32.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 4 days (d) 11 days
33. 33.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹25 (c) ₹50 (d) ₹75
34. 34.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 9 days (d) 1 day
35. 35.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 27 days (d) 26 days
36. 36.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 3 days (d) 27 days
37. 37.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 8 days (d) 11 days
38. 38.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 55 days (b) 19 days (c) 54 days (d) 5 days
39. 39.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 34 days (d) 33 days
40. 40.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹88 (b) ₹110 (c) ₹99 (d) ₹22

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