Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 850 · 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 pens cost ₹9, how much do 8 pens cost? (a) ₹27 (b) ₹14 (c) ₹72 (d) ₹24
2. 2.If 2 pens cost ₹28, how much do 11 pens cost? (a) ₹168 (b) ₹154 (c) ₹37 (d) ₹308
3. 3.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 10 days
4. 4.If 7 pens cost ₹168, how much do 10 pens cost? (a) ₹240 (b) ₹1680 (c) ₹264 (d) ₹171
5. 5.If 2 mangoes cost ₹26, how much do 5 mangoes cost? (a) ₹130 (b) ₹29 (c) ₹65 (d) ₹78
6. 6.If 8 notebooks cost ₹200, how much do 4 notebooks cost? (a) ₹125 (b) ₹100 (c) ₹800 (d) ₹196
7. 7.If 5 pens cost ₹75, how much do 8 pens cost? (a) ₹120 (b) ₹600 (c) ₹135 (d) ₹78
8. 8.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 8 days (d) 10 days
9. 9.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹18 (b) ₹13 (c) ₹24 (d) ₹36
10. 10.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 2 days (d) 8 days
11. 11.If 6 pens cost ₹30, how much do 10 pens cost? (a) ₹300 (b) ₹50 (c) ₹34 (d) ₹55
12. 12.If 6 kites cost ₹18, how much do 7 kites cost? (a) ₹24 (b) ₹126 (c) ₹21 (d) ₹19
13. 13.If 2 pens cost ₹10, how much do 7 pens cost? (a) ₹70 (b) ₹35 (c) ₹15 (d) ₹40
14. 14.If 5 pens cost ₹70, how much do 4 pens cost? (a) ₹56 (b) ₹70 (c) ₹280 (d) ₹69
15. 15.5 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) 4 days (d) 5 days
16. 16.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 17 days (d) 4 days
17. 17.If 6 pens cost ₹36, how much do 2 pens cost? (a) ₹18 (b) ₹12 (c) ₹72 (d) ₹32
18. 18.If 9 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹180 (b) ₹25 (c) ₹40 (d) ₹20
19. 19.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 2 days (d) 14 days
20. 20.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹92 (b) ₹230 (c) ₹46 (d) ₹161
21. 21.If 4 kites cost ₹92, how much do 10 kites cost? (a) ₹98 (b) ₹230 (c) ₹253 (d) ₹920
22. 22.If 2 notebooks cost ₹18, how much do 3 notebooks cost? (a) ₹19 (b) ₹54 (c) ₹27 (d) ₹36
23. 23.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 16 days (d) 12 days
24. 24.If 5 pens cost ₹30, how much do 2 pens cost? (a) ₹60 (b) ₹18 (c) ₹27 (d) ₹12
25. 25.If 4 pens cost ₹100, how much do 10 pens cost? (a) ₹275 (b) ₹106 (c) ₹250 (d) ₹1000
26. 26.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 13 days (d) 17 days
27. 27.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹324 (b) ₹180 (c) ₹252 (d) ₹36
28. 28.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹108 (d) ₹81
29. 29.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 18 days (d) 28 days
30. 30.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 8 days (d) 7 days
31. 31.₹500 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹150 (b) ₹50 (c) ₹250 (d) ₹350
32. 32.If 8 kites cost ₹88, how much do 12 kites cost? (a) ₹1056 (b) ₹92 (c) ₹132 (d) ₹143
33. 33.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
34. 34.If 6 kites cost ₹120, how much do 8 kites cost? (a) ₹122 (b) ₹960 (c) ₹180 (d) ₹160
35. 35.If 2 pens cost ₹18, how much do 4 pens cost? (a) ₹72 (b) ₹45 (c) ₹20 (d) ₹36
36. 36.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹30 (d) ₹20
37. 37.If 2 kites cost ₹38, how much do 7 kites cost? (a) ₹266 (b) ₹43 (c) ₹133 (d) ₹152
38. 38.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 19 days (c) 27 days (d) 11 days
39. 39.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹60 (d) ₹45
40. 40.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 20 days (d) 6 days

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