Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 147 · 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.₹280 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹140 (b) ₹196 (c) ₹84 (d) ₹28
2. 2.If 2 pens cost ₹20, how much do 5 pens cost? (a) ₹60 (b) ₹100 (c) ₹23 (d) ₹50
3. 3.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 2 days (d) 1 day
4. 4.If 3 notebooks cost ₹54, how much do 11 notebooks cost? (a) ₹62 (b) ₹594 (c) ₹216 (d) ₹198
5. 5.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹266 (d) ₹171
6. 6.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 7 days
7. 7.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 5 days (d) 11 days
8. 8.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 4 days (d) 3 days
9. 9.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 27 days (c) 10 days (d) 26 days
10. 10.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹172 (d) ₹430
11. 11.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹126 (c) ₹36 (d) ₹144
12. 12.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 21 days (d) 13 days
13. 13.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 19 days (c) 11 days (d) 9 days
14. 14.If 2 kites cost ₹46, how much do 9 kites cost? (a) ₹414 (b) ₹230 (c) ₹207 (d) ₹53
15. 15.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 9 days (d) 19 days
16. 16.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 4 days (d) 5 days
17. 17.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹18 (b) ₹54 (c) ₹126 (d) ₹90
18. 18.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 41 days (b) 16 days (c) 4 days (d) 40 days
19. 19.If 5 mangoes cost ₹75, how much do 6 mangoes cost? (a) ₹450 (b) ₹105 (c) ₹90 (d) ₹76
20. 20.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 4 days (d) 11 days
21. 21.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹39 (b) ₹30 (c) ₹48 (d) ₹6
22. 22.8 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
23. 23.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹25 (b) ₹175 (c) ₹150 (d) ₹151
24. 24.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹231 (b) ₹42 (c) ₹84 (d) ₹378
25. 25.If 3 pens cost ₹75, how much do 8 pens cost? (a) ₹225 (b) ₹600 (c) ₹200 (d) ₹80
26. 26.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days
27. 27.If 3 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹84 (b) ₹35 (c) ₹22 (d) ₹28
28. 28.₹72 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹36 (d) ₹54
29. 29.If 3 notebooks cost ₹63, how much do 9 notebooks cost? (a) ₹210 (b) ₹567 (c) ₹189 (d) ₹69
30. 30.If 8 notebooks cost ₹96, how much do 3 notebooks cost? (a) ₹36 (b) ₹288 (c) ₹48 (d) ₹91
31. 31.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹185 (d) ₹148
32. 32.If 5 mangoes cost ₹75, how much do 10 mangoes cost? (a) ₹150 (b) ₹750 (c) ₹80 (d) ₹165
33. 33.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹95 (b) ₹77 (c) ₹76 (d) ₹19
34. 34.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 15 days (d) 26 days
35. 35.If 4 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹104 (b) ₹96 (c) ₹40 (d) ₹384
36. 36.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 13 days
37. 37.If 6 pens cost ₹48, how much do 10 pens cost? (a) ₹480 (b) ₹52 (c) ₹80 (d) ₹88
38. 38.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 29 days (c) 28 days (d) 8 days
39. 39.If 8 pens cost ₹136, how much do 10 pens cost? (a) ₹1360 (b) ₹187 (c) ₹138 (d) ₹170
40. 40.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 13 days (d) 9 days

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