Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 760 · 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 9 pens cost ₹72, how much do 12 pens cost? (a) ₹864 (b) ₹75 (c) ₹104 (d) ₹96
2. 2.If 8 kites cost ₹184, how much do 4 kites cost? (a) ₹115 (b) ₹736 (c) ₹92 (d) ₹180
3. 3.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
4. 4.If 5 pens cost ₹65, how much do 2 pens cost? (a) ₹62 (b) ₹26 (c) ₹39 (d) ₹130
5. 5.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 10 days (d) 9 days
6. 6.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹98 (b) ₹28 (c) ₹56 (d) ₹140
7. 7.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹88 (b) ₹32 (c) ₹16 (d) ₹144
8. 8.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 11 days (d) 16 days
9. 9.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 13 days (d) 3 days
10. 10.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 25 days (d) 9 days
11. 11.If 5 kites cost ₹55, how much do 8 kites cost? (a) ₹440 (b) ₹58 (c) ₹99 (d) ₹88
12. 12.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 49 days (d) 9 days
13. 13.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹280 (c) ₹240 (d) ₹40
14. 14.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹40 (d) ₹20
15. 15.If 7 mangoes cost ₹42, how much do 10 mangoes cost? (a) ₹66 (b) ₹420 (c) ₹45 (d) ₹60
16. 16.If 3 kites cost ₹33, how much do 2 kites cost? (a) ₹33 (b) ₹66 (c) ₹22 (d) ₹32
17. 17.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹72 (b) ₹63 (c) ₹9 (d) ₹36
18. 18.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹252 (b) ₹36 (c) ₹180 (d) ₹216
19. 19.If 3 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹126 (b) ₹42 (c) ₹62 (d) ₹63
20. 20.If 6 kites cost ₹42, how much do 9 kites cost? (a) ₹45 (b) ₹378 (c) ₹70 (d) ₹63
21. 21.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 6 days (d) 16 days
22. 22.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
23. 23.If 9 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹16 (b) ₹65 (c) ₹24 (d) ₹144
24. 24.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹266 (b) ₹228 (c) ₹190 (d) ₹38
25. 25.If 3 mangoes cost ₹45, how much do 2 mangoes cost? (a) ₹45 (b) ₹44 (c) ₹30 (d) ₹90
26. 26.If 9 mangoes cost ₹81, how much do 4 mangoes cost? (a) ₹76 (b) ₹36 (c) ₹45 (d) ₹324
27. 27.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹117 (c) ₹78 (d) ₹79
28. 28.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 27 days (d) 15 days
29. 29.₹78 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹13 (d) ₹39
30. 30.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 1 day
31. 31.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹120 (b) ₹60 (c) ₹12 (d) ₹108
32. 32.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 5 days
33. 33.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 20 days (d) 5 days
34. 34.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 9 days (d) 13 days
35. 35.If 5 pens cost ₹120, how much do 6 pens cost? (a) ₹121 (b) ₹720 (c) ₹168 (d) ₹144
36. 36.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹153 (b) ₹17 (c) ₹170 (d) ₹68
37. 37.If 2 pens cost ₹18, how much do 7 pens cost? (a) ₹126 (b) ₹72 (c) ₹63 (d) ₹23
38. 38.If 3 notebooks cost ₹15, how much do 5 notebooks cost? (a) ₹75 (b) ₹25 (c) ₹30 (d) ₹17
39. 39.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 8 days (c) 23 days (d) 14 days
40. 40.If 8 mangoes cost ₹152, how much do 9 mangoes cost? (a) ₹171 (b) ₹153 (c) ₹190 (d) ₹1368

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