Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 71 · 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 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 14 days (d) 18 days
2. 2.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹133 (b) ₹38 (c) ₹152 (d) ₹114
3. 3.If 2 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹80 (b) ₹60 (c) ₹41 (d) ₹120
4. 4.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹250 (b) ₹225 (c) ₹100 (d) ₹25
5. 5.If 6 pens cost ₹18, how much do 7 pens cost? (a) ₹21 (b) ₹19 (c) ₹24 (d) ₹126
6. 6.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹35 (c) ₹30 (d) ₹5
7. 7.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹10 (b) ₹45 (c) ₹90 (d) ₹80
8. 8.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹16 (c) ₹12 (d) ₹8
9. 9.If 8 kites cost ₹168, how much do 2 kites cost? (a) ₹63 (b) ₹336 (c) ₹162 (d) ₹42
10. 10.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹60 (d) ₹100
11. 11.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 13 days (d) 22 days
12. 12.If 9 notebooks cost ₹81, how much do 12 notebooks cost? (a) ₹108 (b) ₹117 (c) ₹972 (d) ₹84
13. 13.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 10 days (d) 12 days
14. 14.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹192 (d) ₹120
15. 15.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 4 days (d) 5 days
16. 16.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 53 days (c) 7 days (d) 52 days
17. 17.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹9 (b) ₹54 (c) ₹45 (d) ₹27
18. 18.9 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) 8 days (d) 9 days
19. 19.4 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
20. 20.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹273 (b) ₹195 (c) ₹39 (d) ₹234
21. 21.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹161 (d) ₹184
22. 22.If 5 kites cost ₹75, how much do 8 kites cost? (a) ₹78 (b) ₹120 (c) ₹600 (d) ₹135
23. 23.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 5 days (d) 45 days
24. 24.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 12 days (d) 8 days
25. 25.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 14 days
26. 26.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹12 (b) ₹36 (c) ₹96 (d) ₹66
27. 27.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹90 (b) ₹30 (c) ₹150 (d) ₹120
28. 28.If 2 pens cost ₹8, how much do 12 pens cost? (a) ₹48 (b) ₹96 (c) ₹18 (d) ₹52
29. 29.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹162 (d) ₹135
30. 30.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 6 days (d) 18 days
31. 31.If 6 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹37 (b) ₹48 (c) ₹252 (d) ₹42
32. 32.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 9 days (d) 26 days
33. 33.If 7 notebooks cost ₹161, how much do 2 notebooks cost? (a) ₹322 (b) ₹46 (c) ₹156 (d) ₹69
34. 34.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹36 (d) ₹48
35. 35.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹210 (b) ₹273 (c) ₹42 (d) ₹336
36. 36.₹319 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹261 (b) ₹58 (c) ₹29 (d) ₹290
37. 37.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹288 (d) ₹224
38. 38.If 7 notebooks cost ₹119, how much do 8 notebooks cost? (a) ₹153 (b) ₹136 (c) ₹120 (d) ₹952
39. 39.If 7 kites cost ₹175, how much do 12 kites cost? (a) ₹180 (b) ₹300 (c) ₹325 (d) ₹2100
40. 40.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 5 days

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