Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 42 · 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. 1.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 8 days (d) 7 days
2. 2.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 10 days (d) 9 days
3. 3.If 2 mangoes cost ₹14, how much do 11 mangoes cost? (a) ₹23 (b) ₹154 (c) ₹77 (d) ₹84
4. 4.If 3 pens cost ₹45, how much do 8 pens cost? (a) ₹50 (b) ₹360 (c) ₹135 (d) ₹120
5. 5.If 5 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹120 (b) ₹30 (c) ₹24 (d) ₹29
6. 6.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 5 days (d) 7 days
7. 7.If 8 kites cost ₹160, how much do 2 kites cost? (a) ₹40 (b) ₹60 (c) ₹154 (d) ₹320
8. 8.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 55 days (c) 19 days (d) 54 days
9. 9.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹87 (b) ₹116 (c) ₹145 (d) ₹29
10. 10.If 9 mangoes cost ₹216, how much do 5 mangoes cost? (a) ₹212 (b) ₹144 (c) ₹1080 (d) ₹120
11. 11.If 2 pens cost ₹40, how much do 8 pens cost? (a) ₹180 (b) ₹320 (c) ₹160 (d) ₹46
12. 12.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 9 days (d) 15 days
13. 13.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹25 (b) ₹125 (c) ₹150 (d) ₹50
14. 14.If 8 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹24 (b) ₹128 (c) ₹16 (d) ₹58
15. 15.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹10 (d) ₹15
16. 16.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹128 (b) ₹208 (c) ₹32 (d) ₹288
17. 17.If 8 pens cost ₹176, how much do 5 pens cost? (a) ₹173 (b) ₹132 (c) ₹880 (d) ₹110
18. 18.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹70 (d) ₹90
19. 19.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹29 (b) ₹56 (c) ₹84 (d) ₹42
20. 20.If 3 pens cost ₹54, how much do 5 pens cost? (a) ₹56 (b) ₹270 (c) ₹108 (d) ₹90
21. 21.If 2 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹45 (b) ₹20 (c) ₹36 (d) ₹72
22. 22.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹288 (d) ₹160
23. 23.If 6 pens cost ₹144, how much do 7 pens cost? (a) ₹1008 (b) ₹145 (c) ₹192 (d) ₹168
24. 24.If 9 pens cost ₹45, how much do 4 pens cost? (a) ₹25 (b) ₹40 (c) ₹20 (d) ₹180
25. 25.If 5 pens cost ₹60, how much do 2 pens cost? (a) ₹24 (b) ₹57 (c) ₹120 (d) ₹36
26. 26.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹176 (b) ₹308 (c) ₹352 (d) ₹44
27. 27.If 8 kites cost ₹24, how much do 12 kites cost? (a) ₹28 (b) ₹36 (c) ₹39 (d) ₹288
28. 28.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 12 days (d) 6 days
29. 29.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 15 days (d) 11 days
30. 30.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 27 days (c) 28 days (d) 17 days
31. 31.If 4 kites cost ₹92, how much do 6 kites cost? (a) ₹552 (b) ₹94 (c) ₹161 (d) ₹138
32. 32.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 6 days (d) 5 days
33. 33.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 3 days
34. 34.If 8 pens cost ₹48, how much do 12 pens cost? (a) ₹78 (b) ₹52 (c) ₹576 (d) ₹72
35. 35.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹252 (b) ₹288 (c) ₹144 (d) ₹36
36. 36.If 6 pens cost ₹42, how much do 7 pens cost? (a) ₹43 (b) ₹56 (c) ₹49 (d) ₹294
37. 37.If 8 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹21 (b) ₹168 (c) ₹51 (d) ₹28
38. 38.If 7 kites cost ₹63, how much do 8 kites cost? (a) ₹81 (b) ₹504 (c) ₹72 (d) ₹64
39. 39.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 9 days (d) 49 days
40. 40.If 8 notebooks cost ₹192, how much do 9 notebooks cost? (a) ₹240 (b) ₹1728 (c) ₹216 (d) ₹193

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