Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 475 · 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.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹66 (b) ₹48 (c) ₹84 (d) ₹12
2. 2.If 9 notebooks cost ₹144, how much do 8 notebooks cost? (a) ₹1152 (b) ₹128 (c) ₹144 (d) ₹143
3. 3.If 2 notebooks cost ₹32, how much do 10 notebooks cost? (a) ₹320 (b) ₹160 (c) ₹176 (d) ₹40
4. 4.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 15 days (d) 6 days
5. 5.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 3 days (d) 2 days
6. 6.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹91 (b) ₹39 (c) ₹65 (d) ₹13
7. 7.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹84 (b) ₹12 (c) ₹72 (d) ₹60
8. 8.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹180 (b) ₹30 (c) ₹165 (d) ₹150
9. 9.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 12 days (d) 11 days
10. 10.If 8 kites cost ₹160, how much do 5 kites cost? (a) ₹157 (b) ₹100 (c) ₹800 (d) ₹120
11. 11.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 16 days (c) 13 days (d) 1 day
12. 12.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 31 days (d) 30 days
13. 13.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 18 days (d) 15 days
14. 14.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 13 days (d) 14 days
15. 15.If 9 notebooks cost ₹81, how much do 10 notebooks cost? (a) ₹82 (b) ₹99 (c) ₹810 (d) ₹90
16. 16.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
17. 17.₹180 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹45 (b) ₹135 (c) ₹180 (d) ₹90
18. 18.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 3 days (d) 5 days
19. 19.₹369 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹246 (b) ₹41 (c) ₹205 (d) ₹164
20. 20.If 2 pens cost ₹48, how much do 11 pens cost? (a) ₹57 (b) ₹288 (c) ₹528 (d) ₹264
21. 21.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
22. 22.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 12 days (d) 11 days
23. 23.If 3 notebooks cost ₹60, how much do 6 notebooks cost? (a) ₹360 (b) ₹63 (c) ₹120 (d) ₹140
24. 24.If 6 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹50 (b) ₹18 (c) ₹108 (d) ₹27
25. 25.If 3 kites cost ₹60, how much do 8 kites cost? (a) ₹480 (b) ₹160 (c) ₹65 (d) ₹180
26. 26.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹75 (d) ₹90
27. 27.If 2 pens cost ₹14, how much do 6 pens cost? (a) ₹49 (b) ₹18 (c) ₹84 (d) ₹42
28. 28.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 18 days (d) 10 days
29. 29.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 40 days (d) 39 days
30. 30.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 27 days (d) 26 days
31. 31.If 3 kites cost ₹66, how much do 12 kites cost? (a) ₹75 (b) ₹286 (c) ₹264 (d) ₹792
32. 32.If 4 notebooks cost ₹100, how much do 5 notebooks cost? (a) ₹500 (b) ₹150 (c) ₹125 (d) ₹101
33. 33.₹322 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹322 (b) ₹276 (c) ₹46 (d) ₹161
34. 34.If 5 pens cost ₹100, how much do 4 pens cost? (a) ₹400 (b) ₹80 (c) ₹100 (d) ₹99
35. 35.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 13 days (d) 15 days
36. 36.If 5 kites cost ₹20, how much do 6 kites cost? (a) ₹120 (b) ₹28 (c) ₹21 (d) ₹24
37. 37.If 5 mangoes cost ₹35, how much do 2 mangoes cost? (a) ₹14 (b) ₹70 (c) ₹21 (d) ₹32
38. 38.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹72 (c) ₹36 (d) ₹108
39. 39.If 7 notebooks cost ₹63, how much do 10 notebooks cost? (a) ₹90 (b) ₹630 (c) ₹99 (d) ₹66
40. 40.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 11 days (d) 26 days

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