Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 827 · 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 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 24 days (d) 6 days
2. 2.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 16 days (d) 17 days
3. 3.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 2 days (d) 3 days
4. 4.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 15 days
5. 5.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹62 (b) ₹124 (c) ₹31 (d) ₹93
6. 6.If 3 mangoes cost ₹39, how much do 12 mangoes cost? (a) ₹156 (b) ₹169 (c) ₹48 (d) ₹468
7. 7.If 5 pens cost ₹20, how much do 3 pens cost? (a) ₹60 (b) ₹18 (c) ₹12 (d) ₹16
8. 8.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹105 (d) ₹75
9. 9.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹29 (b) ₹58 (c) ₹87 (d) ₹116
10. 10.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹5 (c) ₹30 (d) ₹25
11. 11.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 8 days (d) 7 days
12. 12.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹238 (b) ₹187 (c) ₹136 (d) ₹34
13. 13.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹31 (b) ₹279 (c) ₹249 (d) ₹248
14. 14.If 2 notebooks cost ₹40, how much do 4 notebooks cost? (a) ₹42 (b) ₹160 (c) ₹80 (d) ₹100
15. 15.If 9 pens cost ₹63, how much do 12 pens cost? (a) ₹91 (b) ₹756 (c) ₹66 (d) ₹84
16. 16.₹360 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹360 (b) ₹36 (c) ₹324 (d) ₹180
17. 17.If 9 pens cost ₹135, how much do 8 pens cost? (a) ₹134 (b) ₹120 (c) ₹135 (d) ₹1080
18. 18.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹72 (b) ₹84 (c) ₹96 (d) ₹24
19. 19.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹180 (b) ₹165 (c) ₹30 (d) ₹150
20. 20.If 4 pens cost ₹12, how much do 8 pens cost? (a) ₹27 (b) ₹24 (c) ₹96 (d) ₹16
21. 21.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹80 (d) ₹100
22. 22.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 19 days (d) 39 days
23. 23.If 9 pens cost ₹36, how much do 6 pens cost? (a) ₹28 (b) ₹24 (c) ₹33 (d) ₹216
24. 24.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 12 days (d) 3 days
25. 25.If 3 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹84 (b) ₹40 (c) ₹252 (d) ₹96
26. 26.If 9 pens cost ₹36, how much do 4 pens cost? (a) ₹20 (b) ₹31 (c) ₹144 (d) ₹16
27. 27.If 4 pens cost ₹48, how much do 12 pens cost? (a) ₹144 (b) ₹56 (c) ₹156 (d) ₹576
28. 28.₹176 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹16 (b) ₹88 (c) ₹112 (d) ₹64
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.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹88 (d) ₹144
31. 31.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 12 days (c) 23 days (d) 24 days
32. 32.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 3 days (d) 11 days
33. 33.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 2 days (d) 8 days
34. 34.If 6 mangoes cost ₹66, how much do 8 mangoes cost? (a) ₹528 (b) ₹68 (c) ₹99 (d) ₹88
35. 35.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 6 days (d) 7 days
36. 36.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 5 days (c) 45 days (d) 7 days
37. 37.If 9 pens cost ₹27, how much do 10 pens cost? (a) ₹28 (b) ₹33 (c) ₹30 (d) ₹270
38. 38.If 2 pens cost ₹20, how much do 6 pens cost? (a) ₹120 (b) ₹70 (c) ₹24 (d) ₹60
39. 39.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹55 (b) ₹27 (c) ₹54 (d) ₹81
40. 40.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹308 (b) ₹44 (c) ₹264 (d) ₹154

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