Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 267 · 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.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹390 (b) ₹351 (c) ₹156 (d) ₹39
2. 2.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹27 (b) ₹54 (c) ₹19 (d) ₹36
3. 3.₹396 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹36 (b) ₹252 (c) ₹198 (d) ₹144
4. 4.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹112 (c) ₹63 (d) ₹14
5. 5.If 2 kites cost ₹20, how much do 8 kites cost? (a) ₹90 (b) ₹160 (c) ₹80 (d) ₹26
6. 6.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 17 days (d) 27 days
7. 7.If 4 pens cost ₹24, how much do 12 pens cost? (a) ₹78 (b) ₹288 (c) ₹32 (d) ₹72
8. 8.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 2 days
9. 9.If 5 notebooks cost ₹60, how much do 6 notebooks cost? (a) ₹360 (b) ₹61 (c) ₹72 (d) ₹84
10. 10.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹25 (c) ₹10 (d) ₹50
11. 11.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 3 days (c) 36 days (d) 15 days
12. 12.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 23 days (c) 15 days (d) 22 days
13. 13.If 7 pens cost ₹112, how much do 6 pens cost? (a) ₹96 (b) ₹672 (c) ₹112 (d) ₹111
14. 14.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹17 (d) ₹51
15. 15.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 11 days
16. 16.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 2 days
17. 17.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹47 (b) ₹141 (c) ₹188 (d) ₹235
18. 18.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 13 days (d) 15 days
19. 19.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 1 day (d) 2 days
20. 20.If 6 notebooks cost ₹96, how much do 3 notebooks cost? (a) ₹288 (b) ₹48 (c) ₹93 (d) ₹64
21. 21.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹81 (d) ₹27
22. 22.If 2 pens cost ₹36, how much do 7 pens cost? (a) ₹252 (b) ₹41 (c) ₹144 (d) ₹126
23. 23.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹80 (d) ₹55
24. 24.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹312 (b) ₹78 (c) ₹273 (d) ₹39
25. 25.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹27 (c) ₹36 (d) ₹54
26. 26.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 1 day (d) 7 days
27. 27.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 27 days (c) 3 days (d) 15 days
28. 28.If 3 pens cost ₹60, how much do 2 pens cost? (a) ₹59 (b) ₹120 (c) ₹60 (d) ₹40
29. 29.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 10 days (d) 9 days
30. 30.If 9 kites cost ₹99, how much do 3 kites cost? (a) ₹93 (b) ₹297 (c) ₹44 (d) ₹33
31. 31.If 4 pens cost ₹68, how much do 5 pens cost? (a) ₹85 (b) ₹340 (c) ₹69 (d) ₹102
32. 32.If 4 notebooks cost ₹44, how much do 10 notebooks cost? (a) ₹121 (b) ₹440 (c) ₹50 (d) ₹110
33. 33.If 7 pens cost ₹175, how much do 5 pens cost? (a) ₹173 (b) ₹125 (c) ₹150 (d) ₹875
34. 34.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 8 days (d) 9 days
35. 35.If 7 pens cost ₹56, how much do 9 pens cost? (a) ₹72 (b) ₹504 (c) ₹80 (d) ₹58
36. 36.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹450 (b) ₹500 (c) ₹250 (d) ₹50
37. 37.If 3 pens cost ₹51, how much do 9 pens cost? (a) ₹57 (b) ₹170 (c) ₹153 (d) ₹459
38. 38.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 9 days (d) 8 days
39. 39.If 5 pens cost ₹25, how much do 7 pens cost? (a) ₹27 (b) ₹175 (c) ₹35 (d) ₹40
40. 40.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 18 days (d) 2 days

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