Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 737 · 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.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹75 (b) ₹105 (c) ₹90 (d) ₹15
2. 2.If 9 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹42 (b) ₹270 (c) ₹35 (d) ₹30
3. 3.If 5 pens cost ₹85, how much do 4 pens cost? (a) ₹68 (b) ₹340 (c) ₹84 (d) ₹85
4. 4.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 13 days (d) 9 days
5. 5.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 41 days (b) 4 days (c) 16 days (d) 40 days
6. 6.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹215 (d) ₹172
7. 7.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 15 days (d) 9 days
8. 8.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 1 day
9. 9.If 6 pens cost ₹78, how much do 10 pens cost? (a) ₹82 (b) ₹130 (c) ₹780 (d) ₹143
10. 10.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 12 days (d) 28 days
11. 11.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 9 days (d) 5 days
12. 12.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹392 (b) ₹441 (c) ₹49 (d) ₹393
13. 13.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 4 days (d) 2 days
14. 14.If 7 pens cost ₹154, how much do 9 pens cost? (a) ₹198 (b) ₹220 (c) ₹156 (d) ₹1386
15. 15.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 35 days (c) 36 days (d) 5 days
16. 16.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹147 (b) ₹21 (c) ₹126 (d) ₹105
17. 17.If 9 notebooks cost ₹225, how much do 6 notebooks cost? (a) ₹175 (b) ₹1350 (c) ₹222 (d) ₹150
18. 18.If 5 pens cost ₹85, how much do 8 pens cost? (a) ₹88 (b) ₹136 (c) ₹153 (d) ₹680
19. 19.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 9 days (d) 8 days
20. 20.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 8 days (d) 10 days
21. 21.If 3 pens cost ₹39, how much do 9 pens cost? (a) ₹117 (b) ₹130 (c) ₹45 (d) ₹351
22. 22.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹72 (b) ₹36 (c) ₹25 (d) ₹48
23. 23.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹216 (d) ₹336
24. 24.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 17 days (c) 9 days (d) 39 days
25. 25.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹400 (b) ₹200 (c) ₹50 (d) ₹350
26. 26.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹329 (b) ₹188 (c) ₹47 (d) ₹376
27. 27.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹350 (b) ₹70 (c) ₹315 (d) ₹35
28. 28.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 11 days (d) 10 days
29. 29.If 8 kites cost ₹104, how much do 11 kites cost? (a) ₹156 (b) ₹143 (c) ₹1144 (d) ₹107
30. 30.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹60 (b) ₹270 (c) ₹165 (d) ₹30
31. 31.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 11 days (d) 13 days
32. 32.3 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
33. 33.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 11 days (d) 7 days
34. 34.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹110 (b) ₹180 (c) ₹20 (d) ₹40
35. 35.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹195 (b) ₹117 (c) ₹39 (d) ₹234
36. 36.₹429 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹351 (b) ₹312 (c) ₹117 (d) ₹39
37. 37.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹16 (c) ₹40 (d) ₹8
38. 38.₹126 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹54 (d) ₹63
39. 39.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 4 days (d) 6 days
40. 40.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day

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