Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 742 · 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. 1.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 7 days (d) 28 days
2. 2.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 3 days (d) 27 days
3. 3.If 5 pens cost ₹50, how much do 9 pens cost? (a) ₹450 (b) ₹100 (c) ₹54 (d) ₹90
4. 4.If 4 kites cost ₹44, how much do 9 kites cost? (a) ₹49 (b) ₹110 (c) ₹396 (d) ₹99
5. 5.If 6 notebooks cost ₹90, how much do 4 notebooks cost? (a) ₹75 (b) ₹60 (c) ₹360 (d) ₹88
6. 6.If 9 mangoes cost ₹36, how much do 6 mangoes cost? (a) ₹24 (b) ₹28 (c) ₹216 (d) ₹33
7. 7.If 7 mangoes cost ₹105, how much do 5 mangoes cost? (a) ₹75 (b) ₹90 (c) ₹525 (d) ₹103
8. 8.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹80 (b) ₹32 (c) ₹56 (d) ₹16
9. 9.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 8 days (d) 7 days
10. 10.If 5 mangoes cost ₹50, how much do 8 mangoes cost? (a) ₹90 (b) ₹80 (c) ₹400 (d) ₹53
11. 11.If 3 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹61 (b) ₹180 (c) ₹540 (d) ₹198
12. 12.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 13 days (d) 11 days
13. 13.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 56 days (c) 57 days (d) 20 days
14. 14.If 7 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹54 (b) ₹252 (c) ₹121 (d) ₹36
15. 15.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 4 days (d) 16 days
16. 16.If 6 mangoes cost ₹120, how much do 9 mangoes cost? (a) ₹1080 (b) ₹200 (c) ₹123 (d) ₹180
17. 17.9 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) 9 days (d) 10 days
18. 18.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹13 (b) ₹78 (c) ₹65 (d) ₹91
19. 19.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 61 days (c) 9 days (d) 60 days
20. 20.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 21 days (d) 45 days
21. 21.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 7 days (c) 42 days (d) 17 days
22. 22.If 5 kites cost ₹80, how much do 6 kites cost? (a) ₹81 (b) ₹480 (c) ₹112 (d) ₹96
23. 23.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 6 days (d) 5 days
24. 24.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹18 (b) ₹6 (c) ₹30 (d) ₹24
25. 25.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 2 days (d) 4 days
26. 26.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
27. 27.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 10 days (d) 4 days
28. 28.₹30 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹15 (d) ₹25
29. 29.If 5 pens cost ₹40, how much do 11 pens cost? (a) ₹440 (b) ₹88 (c) ₹96 (d) ₹46
30. 30.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 8 days (d) 7 days
31. 31.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹35 (d) ₹42
32. 32.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹78 (b) ₹234 (c) ₹39 (d) ₹195
33. 33.3 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) 4 days (d) 3 days
34. 34.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 15 days (d) 9 days
35. 35.₹319 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹261 (b) ₹232 (c) ₹29 (d) ₹87
36. 36.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 11 days (d) 12 days
37. 37.If 7 mangoes cost ₹49, how much do 9 mangoes cost? (a) ₹51 (b) ₹441 (c) ₹70 (d) ₹63
38. 38.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹189 (b) ₹27 (c) ₹162 (d) ₹135
39. 39.If 8 notebooks cost ₹104, how much do 3 notebooks cost? (a) ₹312 (b) ₹52 (c) ₹99 (d) ₹39
40. 40.₹126 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹63 (d) ₹98

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