Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 905 · 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. 1.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 11 days (d) 15 days
2. 2.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 18 days (d) 10 days
3. 3.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
4. 4.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹195 (b) ₹273 (c) ₹39 (d) ₹234
5. 5.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 7 days (d) 19 days
6. 6.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 22 days (d) 13 days
7. 7.If 9 pens cost ₹198, how much do 5 pens cost? (a) ₹110 (b) ₹132 (c) ₹194 (d) ₹990
8. 8.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 16 days (d) 4 days
9. 9.If 8 pens cost ₹88, how much do 4 pens cost? (a) ₹44 (b) ₹55 (c) ₹84 (d) ₹352
10. 10.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹18 (c) ₹6 (d) ₹48
11. 11.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹10 (d) ₹15
12. 12.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 63 days (b) 7 days (c) 64 days (d) 21 days
13. 13.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 19 days (d) 13 days
14. 14.₹150 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹105 (d) ₹75
15. 15.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹175 (b) ₹140 (c) ₹141 (d) ₹35
16. 16.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹39 (d) ₹52
17. 17.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹143 (b) ₹52 (c) ₹26 (d) ₹234
18. 18.If 3 notebooks cost ₹60, how much do 12 notebooks cost? (a) ₹260 (b) ₹720 (c) ₹240 (d) ₹69
19. 19.If 3 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹160 (b) ₹140 (c) ₹64 (d) ₹420
20. 20.₹240 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹210 (b) ₹240 (c) ₹120 (d) ₹30
21. 21.₹297 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹297 (b) ₹265 (c) ₹264 (d) ₹33
22. 22.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹40 (b) ₹240 (c) ₹140 (d) ₹280
23. 23.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹5 (d) ₹35
24. 24.If 5 notebooks cost ₹35, how much do 2 notebooks cost? (a) ₹14 (b) ₹32 (c) ₹70 (d) ₹21
25. 25.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 15 days
26. 26.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹224 (d) ₹182
27. 27.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
28. 28.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹258 (b) ₹215 (c) ₹43 (d) ₹129
29. 29.If 7 kites cost ₹49, how much do 9 kites cost? (a) ₹441 (b) ₹70 (c) ₹51 (d) ₹63
30. 30.If 7 pens cost ₹161, how much do 6 pens cost? (a) ₹160 (b) ₹138 (c) ₹161 (d) ₹966
31. 31.If 9 kites cost ₹153, how much do 4 kites cost? (a) ₹148 (b) ₹612 (c) ₹85 (d) ₹68
32. 32.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 28 days (d) 11 days
33. 33.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 14 days (c) 6 days (d) 5 days
34. 34.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 7 days
35. 35.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 7 days (d) 5 days
36. 36.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹33 (d) ₹66
37. 37.If 2 mangoes cost ₹30, how much do 10 mangoes cost? (a) ₹165 (b) ₹38 (c) ₹300 (d) ₹150
38. 38.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 17 days (c) 13 days (d) 16 days
39. 39.If 4 pens cost ₹68, how much do 6 pens cost? (a) ₹102 (b) ₹119 (c) ₹408 (d) ₹70
40. 40.If 3 kites cost ₹63, how much do 7 kites cost? (a) ₹67 (b) ₹441 (c) ₹147 (d) ₹168

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