Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 361 · 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. 1.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 17 days (d) 12 days
2. 2.₹210 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹189 (b) ₹105 (c) ₹210 (d) ₹21
3. 3.If 9 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹44 (b) ₹37 (c) ₹360 (d) ₹40
4. 4.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹13 (b) ₹52 (c) ₹39 (d) ₹26
5. 5.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹138 (d) ₹46
6. 6.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹151 (b) ₹25 (c) ₹150 (d) ₹175
7. 7.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 19 days (d) 18 days
8. 8.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
9. 9.If 6 kites cost ₹72, how much do 12 kites cost? (a) ₹78 (b) ₹144 (c) ₹156 (d) ₹864
10. 10.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹152 (b) ₹95 (c) ₹19 (d) ₹171
11. 11.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹60 (d) ₹61
12. 12.If 4 mangoes cost ₹44, how much do 9 mangoes cost? (a) ₹99 (b) ₹396 (c) ₹110 (d) ₹49
13. 13.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹174 (b) ₹145 (c) ₹29 (d) ₹58
14. 14.If 2 notebooks cost ₹32, how much do 9 notebooks cost? (a) ₹288 (b) ₹39 (c) ₹160 (d) ₹144
15. 15.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹5 (d) ₹21
16. 16.If 3 mangoes cost ₹63, how much do 7 mangoes cost? (a) ₹168 (b) ₹67 (c) ₹147 (d) ₹441
17. 17.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 8 days
18. 18.If 8 pens cost ₹104, how much do 2 pens cost? (a) ₹26 (b) ₹208 (c) ₹98 (d) ₹39
19. 19.If 8 notebooks cost ₹24, how much do 2 notebooks cost? (a) ₹9 (b) ₹18 (c) ₹6 (d) ₹48
20. 20.If 6 kites cost ₹24, how much do 7 kites cost? (a) ₹168 (b) ₹28 (c) ₹25 (d) ₹32
21. 21.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹64 (b) ₹96 (c) ₹48 (d) ₹32
22. 22.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹35 (c) ₹175 (d) ₹210
23. 23.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹114 (d) ₹95
24. 24.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 4 days (d) 9 days
25. 25.If 9 pens cost ₹99, how much do 4 pens cost? (a) ₹396 (b) ₹44 (c) ₹55 (d) ₹94
26. 26.If 4 pens cost ₹68, how much do 10 pens cost? (a) ₹680 (b) ₹187 (c) ₹170 (d) ₹74
27. 27.If 6 kites cost ₹102, how much do 5 kites cost? (a) ₹510 (b) ₹102 (c) ₹85 (d) ₹101
28. 28.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹19 (d) ₹133
29. 29.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 2 days
30. 30.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹299 (b) ₹368 (c) ₹230 (d) ₹46
31. 31.If 9 pens cost ₹198, how much do 12 pens cost? (a) ₹201 (b) ₹286 (c) ₹264 (d) ₹2376
32. 32.If 6 kites cost ₹138, how much do 8 kites cost? (a) ₹184 (b) ₹140 (c) ₹207 (d) ₹1104
33. 33.If 7 mangoes cost ₹35, how much do 10 mangoes cost? (a) ₹55 (b) ₹350 (c) ₹50 (d) ₹38
34. 34.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹228 (b) ₹209 (c) ₹190 (d) ₹38
35. 35.If 2 notebooks cost ₹32, how much do 7 notebooks cost? (a) ₹37 (b) ₹224 (c) ₹128 (d) ₹112
36. 36.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 16 days (d) 15 days
37. 37.If 2 pens cost ₹20, how much do 11 pens cost? (a) ₹220 (b) ₹29 (c) ₹110 (d) ₹120
38. 38.If 7 pens cost ₹91, how much do 3 pens cost? (a) ₹273 (b) ₹52 (c) ₹87 (d) ₹39
39. 39.If 8 kites cost ₹104, how much do 10 kites cost? (a) ₹106 (b) ₹143 (c) ₹1040 (d) ₹130
40. 40.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 10 days (d) 16 days

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