Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 316 · 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. 1.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 3 days
2. 2.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 9 days (c) 13 days (d) 22 days
3. 3.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 8 days (d) 16 days
4. 4.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹24 (c) ₹30 (d) ₹6
5. 5.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 4 days (d) 16 days
6. 6.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 7 days (c) 17 days (d) 43 days
7. 7.If 6 mangoes cost ₹144, how much do 10 mangoes cost? (a) ₹264 (b) ₹1440 (c) ₹148 (d) ₹240
8. 8.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 29 days (c) 13 days (d) 28 days
9. 9.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹112 (b) ₹96 (c) ₹56 (d) ₹16
10. 10.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹266 (b) ₹190 (c) ₹38 (d) ₹342
11. 11.If 2 pens cost ₹36, how much do 10 pens cost? (a) ₹180 (b) ₹198 (c) ₹44 (d) ₹360
12. 12.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹136 (d) ₹119
13. 13.If 9 mangoes cost ₹27, how much do 5 mangoes cost? (a) ₹23 (b) ₹135 (c) ₹15 (d) ₹18
14. 14.If 6 notebooks cost ₹54, how much do 5 notebooks cost? (a) ₹270 (b) ₹53 (c) ₹54 (d) ₹45
15. 15.If 2 kites cost ₹36, how much do 10 kites cost? (a) ₹198 (b) ₹44 (c) ₹360 (d) ₹180
16. 16.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹44 (b) ₹352 (c) ₹286 (d) ₹220
17. 17.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 10 days (d) 19 days
18. 18.If 7 mangoes cost ₹105, how much do 8 mangoes cost? (a) ₹840 (b) ₹120 (c) ₹106 (d) ₹135
19. 19.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
20. 20.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹108 (d) ₹84
21. 21.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 1 day
22. 22.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹72 (b) ₹42 (c) ₹12 (d) ₹84
23. 23.If 3 notebooks cost ₹57, how much do 4 notebooks cost? (a) ₹228 (b) ₹95 (c) ₹58 (d) ₹76
24. 24.If 9 pens cost ₹207, how much do 7 pens cost? (a) ₹205 (b) ₹161 (c) ₹184 (d) ₹1449
25. 25.If 5 mangoes cost ₹125, how much do 9 mangoes cost? (a) ₹1125 (b) ₹129 (c) ₹250 (d) ₹225
26. 26.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 20 days (d) 13 days
27. 27.If 8 mangoes cost ₹32, how much do 4 mangoes cost? (a) ₹28 (b) ₹128 (c) ₹16 (d) ₹20
28. 28.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹140 (c) ₹175 (d) ₹35
29. 29.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 13 days (d) 4 days
30. 30.If 4 pens cost ₹96, how much do 5 pens cost? (a) ₹120 (b) ₹480 (c) ₹144 (d) ₹97
31. 31.If 4 pens cost ₹36, how much do 5 pens cost? (a) ₹45 (b) ₹37 (c) ₹180 (d) ₹54
32. 32.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 5 days (d) 15 days
33. 33.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 20 days (d) 56 days
34. 34.If 9 pens cost ₹207, how much do 4 pens cost? (a) ₹202 (b) ₹115 (c) ₹92 (d) ₹828
35. 35.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹37 (b) ₹144 (c) ₹48 (d) ₹60
36. 36.If 6 pens cost ₹84, how much do 12 pens cost? (a) ₹90 (b) ₹1008 (c) ₹182 (d) ₹168
37. 37.If 4 mangoes cost ₹84, how much do 11 mangoes cost? (a) ₹231 (b) ₹252 (c) ₹924 (d) ₹91
38. 38.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 25 days (d) 4 days
39. 39.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 17 days
40. 40.If 8 mangoes cost ₹176, how much do 9 mangoes cost? (a) ₹1584 (b) ₹177 (c) ₹220 (d) ₹198

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