Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 990 · 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 3 kites cost ₹9, how much do 10 kites cost? (a) ₹16 (b) ₹33 (c) ₹30 (d) ₹90
2. 2.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
3. 3.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 3 days (d) 2 days
4. 4.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹104 (b) ₹80 (c) ₹16 (d) ₹128
5. 5.If 8 notebooks cost ₹120, how much do 10 notebooks cost? (a) ₹165 (b) ₹1200 (c) ₹122 (d) ₹150
6. 6.If 8 mangoes cost ₹136, how much do 3 mangoes cost? (a) ₹131 (b) ₹68 (c) ₹51 (d) ₹408
7. 7.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹35 (c) ₹20 (d) ₹50
8. 8.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹126 (b) ₹56 (c) ₹91 (d) ₹14
9. 9.If 8 kites cost ₹144, how much do 6 kites cost? (a) ₹108 (b) ₹864 (c) ₹142 (d) ₹126
10. 10.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 19 days (d) 27 days
11. 11.If 2 kites cost ₹24, how much do 5 kites cost? (a) ₹72 (b) ₹60 (c) ₹27 (d) ₹120
12. 12.If 8 pens cost ₹168, how much do 5 pens cost? (a) ₹105 (b) ₹165 (c) ₹126 (d) ₹840
13. 13.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹245 (c) ₹49 (d) ₹196
14. 14.If 2 kites cost ₹16, how much do 7 kites cost? (a) ₹64 (b) ₹112 (c) ₹56 (d) ₹21
15. 15.If 5 kites cost ₹25, how much do 3 kites cost? (a) ₹15 (b) ₹20 (c) ₹23 (d) ₹75
16. 16.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹99 (b) ₹11 (c) ₹22 (d) ₹110
17. 17.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹81 (d) ₹135
18. 18.₹637 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹441 (b) ₹49 (c) ₹490 (d) ₹196
19. 19.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹68 (b) ₹170 (c) ₹153 (d) ₹17
20. 20.If 5 pens cost ₹35, how much do 6 pens cost? (a) ₹210 (b) ₹49 (c) ₹42 (d) ₹36
21. 21.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹144 (c) ₹16 (d) ₹128
22. 22.If 9 kites cost ₹72, how much do 2 kites cost? (a) ₹65 (b) ₹144 (c) ₹16 (d) ₹24
23. 23.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹115 (d) ₹138
24. 24.If 9 mangoes cost ₹36, how much do 6 mangoes cost? (a) ₹216 (b) ₹33 (c) ₹24 (d) ₹28
25. 25.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 3 days (d) 11 days
26. 26.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹378 (b) ₹168 (c) ₹273 (d) ₹42
27. 27.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 9 days
28. 28.If 3 notebooks cost ₹54, how much do 9 notebooks cost? (a) ₹180 (b) ₹162 (c) ₹486 (d) ₹60
29. 29.If 3 pens cost ₹48, how much do 5 pens cost? (a) ₹50 (b) ₹240 (c) ₹80 (d) ₹96
30. 30.If 6 mangoes cost ₹108, how much do 12 mangoes cost? (a) ₹234 (b) ₹114 (c) ₹216 (d) ₹1296
31. 31.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 27 days (d) 26 days
32. 32.If 4 kites cost ₹12, how much do 7 kites cost? (a) ₹24 (b) ₹15 (c) ₹21 (d) ₹84
33. 33.If 8 mangoes cost ₹136, how much do 7 mangoes cost? (a) ₹119 (b) ₹136 (c) ₹135 (d) ₹952
34. 34.If 5 notebooks cost ₹110, how much do 6 notebooks cost? (a) ₹132 (b) ₹111 (c) ₹660 (d) ₹154
35. 35.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹10 (b) ₹20 (c) ₹25 (d) ₹30
36. 36.If 5 mangoes cost ₹115, how much do 3 mangoes cost? (a) ₹92 (b) ₹345 (c) ₹69 (d) ₹113
37. 37.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
38. 38.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹24 (c) ₹6 (d) ₹27
39. 39.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 3 days (d) 7 days
40. 40.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 45 days (d) 21 days

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