Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 906 · 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. 1.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 6 days (d) 8 days
2. 2.If 4 kites cost ₹76, how much do 6 kites cost? (a) ₹78 (b) ₹133 (c) ₹456 (d) ₹114
3. 3.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 12 days (d) 24 days
4. 4.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days
5. 5.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹55 (b) ₹99 (c) ₹11 (d) ₹77
6. 6.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 8 days
7. 7.If 6 kites cost ₹24, how much do 3 kites cost? (a) ₹12 (b) ₹16 (c) ₹21 (d) ₹72
8. 8.If 9 mangoes cost ₹144, how much do 3 mangoes cost? (a) ₹432 (b) ₹138 (c) ₹64 (d) ₹48
9. 9.If 6 notebooks cost ₹30, how much do 11 notebooks cost? (a) ₹330 (b) ₹55 (c) ₹35 (d) ₹60
10. 10.If 5 mangoes cost ₹115, how much do 4 mangoes cost? (a) ₹115 (b) ₹114 (c) ₹92 (d) ₹460
11. 11.If 3 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹40 (b) ₹108 (c) ₹36 (d) ₹18
12. 12.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 10 days
13. 13.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 2 days (d) 3 days
14. 14.If 8 kites cost ₹144, how much do 6 kites cost? (a) ₹864 (b) ₹142 (c) ₹126 (d) ₹108
15. 15.If 7 pens cost ₹105, how much do 8 pens cost? (a) ₹135 (b) ₹106 (c) ₹840 (d) ₹120
16. 16.If 4 kites cost ₹76, how much do 9 kites cost? (a) ₹81 (b) ₹684 (c) ₹190 (d) ₹171
17. 17.If 7 notebooks cost ₹175, how much do 6 notebooks cost? (a) ₹1050 (b) ₹175 (c) ₹174 (d) ₹150
18. 18.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 8 days (d) 6 days
19. 19.If 2 mangoes cost ₹20, how much do 9 mangoes cost? (a) ₹27 (b) ₹180 (c) ₹100 (d) ₹90
20. 20.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹185 (b) ₹37 (c) ₹296 (d) ₹333
21. 21.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 22 days (d) 23 days
22. 22.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 5 days (d) 6 days
23. 23.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 11 days
24. 24.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 13 days (c) 5 days (d) 18 days
25. 25.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹156 (b) ₹24 (c) ₹216 (d) ₹96
26. 26.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹33 (b) ₹66 (c) ₹55 (d) ₹11
27. 27.If 8 notebooks cost ₹192, how much do 12 notebooks cost? (a) ₹288 (b) ₹196 (c) ₹2304 (d) ₹312
28. 28.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 4 days (d) 2 days
29. 29.If 6 mangoes cost ₹150, how much do 3 mangoes cost? (a) ₹100 (b) ₹147 (c) ₹450 (d) ₹75
30. 30.If 6 pens cost ₹144, how much do 11 pens cost? (a) ₹288 (b) ₹149 (c) ₹264 (d) ₹1584
31. 31.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 3 days
32. 32.If 9 notebooks cost ₹216, how much do 7 notebooks cost? (a) ₹192 (b) ₹214 (c) ₹168 (d) ₹1512
33. 33.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹75 (d) ₹150
34. 34.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
35. 35.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 17 days (c) 13 days (d) 21 days
36. 36.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 11 days (d) 18 days
37. 37.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 18 days (d) 19 days
38. 38.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 17 days (d) 11 days
39. 39.If 5 notebooks cost ₹15, how much do 10 notebooks cost? (a) ₹33 (b) ₹30 (c) ₹150 (d) ₹20
40. 40.If 8 kites cost ₹24, how much do 6 kites cost? (a) ₹144 (b) ₹21 (c) ₹22 (d) ₹18

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