Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 509 · 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 notebooks cost ₹168, how much do 7 notebooks cost? (a) ₹167 (b) ₹1176 (c) ₹168 (d) ₹147
2. 2.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 8 days (d) 6 days
3. 3.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹24 (d) ₹42
4. 4.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 10 days (d) 8 days
5. 5.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 25 days (d) 13 days
6. 6.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹60 (b) ₹150 (c) ₹135 (d) ₹15
7. 7.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹34 (b) ₹306 (c) ₹170 (d) ₹238
8. 8.If 9 pens cost ₹153, how much do 12 pens cost? (a) ₹1836 (b) ₹221 (c) ₹156 (d) ₹204
9. 9.If 4 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹120 (b) ₹63 (c) ₹105 (d) ₹420
10. 10.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹99 (c) ₹165 (d) ₹33
11. 11.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹11 (b) ₹66 (c) ₹55 (d) ₹77
12. 12.If 3 pens cost ₹39, how much do 7 pens cost? (a) ₹91 (b) ₹43 (c) ₹104 (d) ₹273
13. 13.₹352 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹96 (b) ₹256 (c) ₹176 (d) ₹32
14. 14.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹35 (b) ₹63 (c) ₹70 (d) ₹7
15. 15.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹144 (b) ₹24 (c) ₹120 (d) ₹168
16. 16.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹312 (b) ₹192 (c) ₹48 (d) ₹432
17. 17.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 6 days (d) 12 days
18. 18.If 5 mangoes cost ₹105, how much do 6 mangoes cost? (a) ₹630 (b) ₹126 (c) ₹147 (d) ₹106
19. 19.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 3 days
20. 20.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹147 (b) ₹84 (c) ₹21 (d) ₹168
21. 21.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹55 (d) ₹11
22. 22.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹24 (b) ₹216 (c) ₹120 (d) ₹168
23. 23.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 14 days (d) 5 days
24. 24.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 31 days (c) 30 days (d) 19 days
25. 25.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 4 days
26. 26.If 6 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹61 (b) ₹420 (c) ₹70 (d) ₹80
27. 27.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹210 (b) ₹189 (c) ₹21 (d) ₹42
28. 28.₹418 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹342 (b) ₹76 (c) ₹209 (d) ₹38
29. 29.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹42 (b) ₹29 (c) ₹56 (d) ₹84
30. 30.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹92 (b) ₹69 (c) ₹138 (d) ₹46
31. 31.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹62 (b) ₹248 (c) ₹217 (d) ₹31
32. 32.If 2 pens cost ₹40, how much do 11 pens cost? (a) ₹220 (b) ₹440 (c) ₹240 (d) ₹49
33. 33.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
34. 34.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹5 (d) ₹15
35. 35.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹95 (b) ₹114 (c) ₹133 (d) ₹19
36. 36.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹30 (d) ₹70
37. 37.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹61 (b) ₹240 (c) ₹80 (d) ₹100
38. 38.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 3 days
39. 39.If 5 notebooks cost ₹35, how much do 10 notebooks cost? (a) ₹40 (b) ₹70 (c) ₹77 (d) ₹350
40. 40.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹10 (b) ₹5 (c) ₹15 (d) ₹20

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