Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 92 · 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.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹234 (d) ₹324
2. 2.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 4 days (d) 25 days
3. 3.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 26 days (d) 15 days
4. 4.If 7 pens cost ₹21, how much do 9 pens cost? (a) ₹30 (b) ₹23 (c) ₹189 (d) ₹27
5. 5.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹63 (b) ₹70 (c) ₹56 (d) ₹14
6. 6.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹36 (c) ₹8 (d) ₹16
7. 7.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 5 days (d) 35 days
8. 8.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 42 days (c) 8 days (d) 43 days
9. 9.If 6 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹324 (b) ₹39 (c) ₹60 (d) ₹54
10. 10.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 22 days (d) 21 days
11. 11.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹28 (d) ₹21
12. 12.If 4 kites cost ₹24, how much do 7 kites cost? (a) ₹48 (b) ₹168 (c) ₹27 (d) ₹42
13. 13.If 4 mangoes cost ₹60, how much do 11 mangoes cost? (a) ₹67 (b) ₹165 (c) ₹660 (d) ₹180
14. 14.If 4 pens cost ₹12, how much do 2 pens cost? (a) ₹9 (b) ₹24 (c) ₹10 (d) ₹6
15. 15.If 6 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹432 (b) ₹96 (c) ₹141 (d) ₹72
16. 16.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 17 days
17. 17.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹80 (b) ₹112 (c) ₹16 (d) ₹48
18. 18.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹48 (b) ₹20 (c) ₹16 (d) ₹13
19. 19.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 5 days (d) 20 days
20. 20.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 36 days (c) 6 days (d) 4 days
21. 21.If 6 kites cost ₹36, how much do 3 kites cost? (a) ₹108 (b) ₹33 (c) ₹24 (d) ₹18
22. 22.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹182 (b) ₹252 (c) ₹112 (d) ₹28
23. 23.If 2 pens cost ₹12, how much do 6 pens cost? (a) ₹72 (b) ₹36 (c) ₹16 (d) ₹42
24. 24.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 48 days (b) 3 days (c) 21 days (d) 4 days
25. 25.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 12 days (d) 19 days
26. 26.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹345 (b) ₹387 (c) ₹43 (d) ₹344
27. 27.If 2 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹37 (b) ₹108 (c) ₹54 (d) ₹72
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) 15 days (d) 27 days
29. 29.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
30. 30.If 3 notebooks cost ₹51, how much do 2 notebooks cost? (a) ₹50 (b) ₹102 (c) ₹51 (d) ₹34
31. 31.If 2 kites cost ₹6, how much do 7 kites cost? (a) ₹42 (b) ₹24 (c) ₹21 (d) ₹11
32. 32.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹136 (b) ₹238 (c) ₹34 (d) ₹272
33. 33.If 9 pens cost ₹90, how much do 10 pens cost? (a) ₹91 (b) ₹110 (c) ₹100 (d) ₹900
34. 34.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 13 days (d) 11 days
35. 35.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹18 (b) ₹108 (c) ₹99 (d) ₹90
36. 36.If 6 mangoes cost ₹60, how much do 11 mangoes cost? (a) ₹660 (b) ₹120 (c) ₹110 (d) ₹65
37. 37.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 8 days (d) 7 days
38. 38.If 7 mangoes cost ₹126, how much do 10 mangoes cost? (a) ₹1260 (b) ₹129 (c) ₹198 (d) ₹180
39. 39.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
40. 40.If 4 notebooks cost ₹44, how much do 2 notebooks cost? (a) ₹42 (b) ₹33 (c) ₹88 (d) ₹22

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