Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 609 · 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.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹310 (b) ₹155 (c) ₹279 (d) ₹31
2. 2.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 6 days (d) 7 days
3. 3.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 9 days
4. 4.If 9 pens cost ₹216, how much do 7 pens cost? (a) ₹214 (b) ₹168 (c) ₹192 (d) ₹1512
5. 5.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹500 (b) ₹125 (c) ₹101 (d) ₹150
6. 6.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 4 days (d) 9 days
7. 7.If 6 kites cost ₹90, how much do 9 kites cost? (a) ₹93 (b) ₹810 (c) ₹135 (d) ₹150
8. 8.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 30 days (c) 31 days (d) 19 days
9. 9.If 6 kites cost ₹144, how much do 9 kites cost? (a) ₹240 (b) ₹147 (c) ₹1296 (d) ₹216
10. 10.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹13 (b) ₹130 (c) ₹117 (d) ₹65
11. 11.If 9 pens cost ₹189, how much do 12 pens cost? (a) ₹273 (b) ₹2268 (c) ₹252 (d) ₹192
12. 12.If 6 pens cost ₹90, how much do 10 pens cost? (a) ₹150 (b) ₹165 (c) ₹900 (d) ₹94
13. 13.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹224 (c) ₹28 (d) ₹252
14. 14.₹304 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹152 (b) ₹190 (c) ₹38 (d) ₹114
15. 15.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹112 (b) ₹182 (c) ₹28 (d) ₹252
16. 16.If 7 mangoes cost ₹112, how much do 2 mangoes cost? (a) ₹107 (b) ₹224 (c) ₹48 (d) ₹32
17. 17.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹126 (d) ₹18
18. 18.₹242 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹22 (b) ₹121 (c) ₹154 (d) ₹88
19. 19.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 10 days
20. 20.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 9 days (d) 4 days
21. 21.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 9 days
22. 22.If 9 kites cost ₹117, how much do 8 kites cost? (a) ₹116 (b) ₹104 (c) ₹936 (d) ₹117
23. 23.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹54 (d) ₹60
24. 24.If 2 pens cost ₹14, how much do 3 pens cost? (a) ₹42 (b) ₹28 (c) ₹15 (d) ₹21
25. 25.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹95 (b) ₹114 (c) ₹19 (d) ₹76
26. 26.If 9 pens cost ₹144, how much do 2 pens cost? (a) ₹32 (b) ₹137 (c) ₹288 (d) ₹48
27. 27.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 6 days (d) 4 days
28. 28.If 5 mangoes cost ₹95, how much do 11 mangoes cost? (a) ₹228 (b) ₹209 (c) ₹101 (d) ₹1045
29. 29.If 9 kites cost ₹153, how much do 4 kites cost? (a) ₹68 (b) ₹85 (c) ₹612 (d) ₹148
30. 30.₹120 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹72 (d) ₹60
31. 31.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹279 (c) ₹31 (d) ₹155
32. 32.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 19 days (d) 2 days
33. 33.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹128 (d) ₹112
34. 34.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 15 days (d) 20 days
35. 35.If 4 kites cost ₹32, how much do 7 kites cost? (a) ₹64 (b) ₹35 (c) ₹56 (d) ₹224
36. 36.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 42 days (d) 43 days
37. 37.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 26 days (c) 27 days (d) 28 days
38. 38.If 9 notebooks cost ₹225, how much do 5 notebooks cost? (a) ₹150 (b) ₹221 (c) ₹125 (d) ₹1125
39. 39.If 3 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹432 (b) ₹156 (c) ₹45 (d) ₹144
40. 40.If 2 pens cost ₹50, how much do 8 pens cost? (a) ₹225 (b) ₹200 (c) ₹56 (d) ₹400

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