Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 416 · 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. 1.5 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
2. 2.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 36 days (c) 15 days (d) 37 days
3. 3.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 27 days (d) 3 days
4. 4.₹220 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹110 (b) ₹198 (c) ₹220 (d) ₹22
5. 5.If 5 pens cost ₹85, how much do 10 pens cost? (a) ₹90 (b) ₹170 (c) ₹187 (d) ₹850
6. 6.If 8 pens cost ₹184, how much do 10 pens cost? (a) ₹253 (b) ₹186 (c) ₹1840 (d) ₹230
7. 7.If 4 notebooks cost ₹44, how much do 6 notebooks cost? (a) ₹77 (b) ₹46 (c) ₹66 (d) ₹264
8. 8.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹18 (c) ₹27 (d) ₹54
9. 9.If 4 kites cost ₹12, how much do 11 kites cost? (a) ₹19 (b) ₹36 (c) ₹132 (d) ₹33
10. 10.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 3 days (c) 37 days (d) 15 days
11. 11.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 11 days (d) 8 days
12. 12.If 7 kites cost ₹77, how much do 9 kites cost? (a) ₹110 (b) ₹99 (c) ₹693 (d) ₹79
13. 13.If 7 pens cost ₹42, how much do 10 pens cost? (a) ₹45 (b) ₹420 (c) ₹66 (d) ₹60
14. 14.If 9 notebooks cost ₹81, how much do 12 notebooks cost? (a) ₹117 (b) ₹84 (c) ₹972 (d) ₹108
15. 15.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 13 days (d) 8 days
16. 16.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 15 days (d) 9 days
17. 17.If 9 pens cost ₹72, how much do 7 pens cost? (a) ₹504 (b) ₹64 (c) ₹56 (d) ₹70
18. 18.If 2 mangoes cost ₹14, how much do 12 mangoes cost? (a) ₹168 (b) ₹84 (c) ₹91 (d) ₹24
19. 19.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹112 (d) ₹84
20. 20.If 3 pens cost ₹72, how much do 4 pens cost? (a) ₹288 (b) ₹96 (c) ₹73 (d) ₹120
21. 21.If 7 notebooks cost ₹49, how much do 12 notebooks cost? (a) ₹54 (b) ₹84 (c) ₹588 (d) ₹91
22. 22.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹78 (d) ₹96
23. 23.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 8 days (d) 7 days
24. 24.If 6 pens cost ₹42, how much do 4 pens cost? (a) ₹40 (b) ₹168 (c) ₹28 (d) ₹35
25. 25.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹430 (d) ₹387
26. 26.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹161 (b) ₹138 (c) ₹115 (d) ₹23
27. 27.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 61 days (c) 60 days (d) 21 days
28. 28.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹160 (b) ₹224 (c) ₹32 (d) ₹192
29. 29.If 2 mangoes cost ₹44, how much do 10 mangoes cost? (a) ₹440 (b) ₹52 (c) ₹220 (d) ₹242
30. 30.If 6 notebooks cost ₹102, how much do 4 notebooks cost? (a) ₹85 (b) ₹68 (c) ₹408 (d) ₹100
31. 31.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 3 days
32. 32.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹60 (d) ₹72
33. 33.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 9 days (d) 8 days
34. 34.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 45 days (d) 5 days
35. 35.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 13 days (d) 22 days
36. 36.If 5 pens cost ₹45, how much do 4 pens cost? (a) ₹36 (b) ₹44 (c) ₹45 (d) ₹180
37. 37.If 3 pens cost ₹18, how much do 7 pens cost? (a) ₹126 (b) ₹48 (c) ₹22 (d) ₹42
38. 38.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹27 (b) ₹9 (c) ₹45 (d) ₹36
39. 39.If 8 notebooks cost ₹40, how much do 7 notebooks cost? (a) ₹39 (b) ₹35 (c) ₹280 (d) ₹40
40. 40.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹96 (b) ₹72 (c) ₹24 (d) ₹84

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