Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 409 · 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. 1.3 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) 3 days (d) 4 days
2. 2.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 2 days (c) 3 days (d) 4 days
3. 3.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹20 (c) ₹180 (d) ₹160
4. 4.If 8 pens cost ₹152, how much do 5 pens cost? (a) ₹95 (b) ₹114 (c) ₹760 (d) ₹149
5. 5.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹125 (b) ₹225 (c) ₹200 (d) ₹25
6. 6.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 5 days (d) 4 days
7. 7.If 2 notebooks cost ₹16, how much do 6 notebooks cost? (a) ₹20 (b) ₹96 (c) ₹56 (d) ₹48
8. 8.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹52 (d) ₹39
9. 9.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 13 days (d) 4 days
10. 10.If 2 notebooks cost ₹38, how much do 6 notebooks cost? (a) ₹114 (b) ₹228 (c) ₹133 (d) ₹42
11. 11.If 7 kites cost ₹84, how much do 6 kites cost? (a) ₹83 (b) ₹84 (c) ₹72 (d) ₹504
12. 12.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 2 days
13. 13.₹180 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹20 (b) ₹90 (c) ₹80 (d) ₹100
14. 14.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 48 days (c) 21 days (d) 3 days
15. 15.If 4 pens cost ₹76, how much do 11 pens cost? (a) ₹83 (b) ₹209 (c) ₹836 (d) ₹228
16. 16.3 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
17. 17.If 2 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹300 (b) ₹38 (c) ₹150 (d) ₹165
18. 18.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹110 (b) ₹44 (c) ₹132 (d) ₹88
19. 19.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 6 days (d) 7 days
20. 20.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹18 (b) ₹108 (c) ₹90 (d) ₹54
21. 21.If 6 kites cost ₹60, how much do 7 kites cost? (a) ₹80 (b) ₹420 (c) ₹70 (d) ₹61
22. 22.If 8 mangoes cost ₹64, how much do 7 mangoes cost? (a) ₹64 (b) ₹448 (c) ₹63 (d) ₹56
23. 23.If 2 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹45 (b) ₹88 (c) ₹66 (d) ₹132
24. 24.If 3 kites cost ₹63, how much do 10 kites cost? (a) ₹70 (b) ₹630 (c) ₹231 (d) ₹210
25. 25.If 6 notebooks cost ₹144, how much do 10 notebooks cost? (a) ₹264 (b) ₹240 (c) ₹1440 (d) ₹148
26. 26.If 4 kites cost ₹100, how much do 10 kites cost? (a) ₹106 (b) ₹1000 (c) ₹250 (d) ₹275
27. 27.If 6 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹24 (b) ₹120 (c) ₹20 (d) ₹23
28. 28.If 6 kites cost ₹90, how much do 2 kites cost? (a) ₹180 (b) ₹45 (c) ₹86 (d) ₹30
29. 29.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹208 (b) ₹130 (c) ₹26 (d) ₹169
30. 30.If 4 kites cost ₹84, how much do 10 kites cost? (a) ₹210 (b) ₹840 (c) ₹90 (d) ₹231
31. 31.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹246 (b) ₹287 (c) ₹41 (d) ₹205
32. 32.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹105 (d) ₹135
33. 33.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 11 days (d) 3 days
34. 34.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹231 (b) ₹198 (c) ₹33 (d) ₹199
35. 35.If 3 notebooks cost ₹12, how much do 11 notebooks cost? (a) ₹48 (b) ₹44 (c) ₹20 (d) ₹132
36. 36.If 3 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹24 (b) ₹60 (c) ₹14 (d) ₹20
37. 37.If 4 pens cost ₹24, how much do 6 pens cost? (a) ₹42 (b) ₹26 (c) ₹36 (d) ₹144
38. 38.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹9 (d) ₹27
39. 39.If 3 pens cost ₹12, how much do 7 pens cost? (a) ₹32 (b) ₹16 (c) ₹28 (d) ₹84
40. 40.If 3 notebooks cost ₹72, how much do 4 notebooks cost? (a) ₹120 (b) ₹288 (c) ₹73 (d) ₹96

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