Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 350 · 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.If 8 kites cost ₹32, how much do 10 kites cost? (a) ₹34 (b) ₹44 (c) ₹40 (d) ₹320
2. 2.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 28 days (d) 26 days
3. 3.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹100 (b) ₹75 (c) ₹150 (d) ₹50
4. 4.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹207 (b) ₹230 (c) ₹23 (d) ₹115
5. 5.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹24 (b) ₹168 (c) ₹108 (d) ₹48
6. 6.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹144 (d) ₹180
7. 7.If 9 pens cost ₹153, how much do 7 pens cost? (a) ₹119 (b) ₹136 (c) ₹151 (d) ₹1071
8. 8.If 2 kites cost ₹46, how much do 6 kites cost? (a) ₹276 (b) ₹50 (c) ₹138 (d) ₹161
9. 9.If 5 pens cost ₹95, how much do 6 pens cost? (a) ₹133 (b) ₹114 (c) ₹570 (d) ₹96
10. 10.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹432 (b) ₹48 (c) ₹312 (d) ₹192
11. 11.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹490 (d) ₹441
12. 12.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 4 days (d) 2 days
13. 13.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 16 days (d) 9 days
14. 14.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 15 days (d) 14 days
15. 15.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹72 (b) ₹44 (c) ₹8 (d) ₹16
16. 16.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹98 (d) ₹42
17. 17.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
18. 18.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 1 day (d) 10 days
19. 19.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 5 days (c) 7 days (d) 6 days
20. 20.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
21. 21.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹84 (d) ₹54
22. 22.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹32 (c) ₹36 (d) ₹8
23. 23.If 5 mangoes cost ₹100, how much do 6 mangoes cost? (a) ₹101 (b) ₹140 (c) ₹600 (d) ₹120
24. 24.If 2 notebooks cost ₹12, how much do 3 notebooks cost? (a) ₹36 (b) ₹24 (c) ₹18 (d) ₹13
25. 25.If 8 pens cost ₹144, how much do 12 pens cost? (a) ₹1728 (b) ₹148 (c) ₹234 (d) ₹216
26. 26.If 5 mangoes cost ₹20, how much do 11 mangoes cost? (a) ₹26 (b) ₹48 (c) ₹220 (d) ₹44
27. 27.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 4 days (d) 3 days
28. 28.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 2 days (d) 8 days
29. 29.If 5 mangoes cost ₹125, how much do 12 mangoes cost? (a) ₹325 (b) ₹300 (c) ₹1500 (d) ₹132
30. 30.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹46 (b) ₹253 (c) ₹322 (d) ₹184
31. 31.If 4 pens cost ₹20, how much do 2 pens cost? (a) ₹40 (b) ₹15 (c) ₹10 (d) ₹18
32. 32.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 9 days (d) 49 days
33. 33.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 11 days (d) 18 days
34. 34.If 8 pens cost ₹168, how much do 9 pens cost? (a) ₹169 (b) ₹1512 (c) ₹189 (d) ₹210
35. 35.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
36. 36.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 7 days (d) 10 days
37. 37.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 1 day
38. 38.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹96 (b) ₹192 (c) ₹144 (d) ₹48
39. 39.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 15 days (d) 17 days
40. 40.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 21 days (d) 9 days

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