Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 377 · 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. 1.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 5 days (d) 13 days
2. 2.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹441 (d) ₹343
3. 3.If 7 notebooks cost ₹42, how much do 6 notebooks cost? (a) ₹42 (b) ₹41 (c) ₹36 (d) ₹252
4. 4.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 31 days (c) 30 days (d) 12 days
5. 5.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹48 (b) ₹30 (c) ₹39 (d) ₹6
6. 6.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹170 (b) ₹204 (c) ₹34 (d) ₹238
7. 7.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 10 days (d) 14 days
8. 8.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹22 (b) ₹132 (c) ₹110 (d) ₹121
9. 9.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 5 days
10. 10.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 12 days (d) 16 days
11. 11.If 9 mangoes cost ₹153, how much do 10 mangoes cost? (a) ₹1530 (b) ₹170 (c) ₹187 (d) ₹154
12. 12.If 8 kites cost ₹112, how much do 9 kites cost? (a) ₹1008 (b) ₹140 (c) ₹113 (d) ₹126
13. 13.If 7 pens cost ₹112, how much do 11 pens cost? (a) ₹1232 (b) ₹176 (c) ₹192 (d) ₹116
14. 14.If 9 kites cost ₹63, how much do 2 kites cost? (a) ₹126 (b) ₹21 (c) ₹14 (d) ₹56
15. 15.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 3 days
16. 16.If 8 pens cost ₹96, how much do 6 pens cost? (a) ₹72 (b) ₹576 (c) ₹94 (d) ₹84
17. 17.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 1 day
18. 18.If 3 kites cost ₹18, how much do 12 kites cost? (a) ₹72 (b) ₹27 (c) ₹216 (d) ₹78
19. 19.If 9 kites cost ₹171, how much do 7 kites cost? (a) ₹1197 (b) ₹169 (c) ₹152 (d) ₹133
20. 20.₹210 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹63 (d) ₹147
21. 21.If 5 kites cost ₹45, how much do 9 kites cost? (a) ₹405 (b) ₹81 (c) ₹90 (d) ₹49
22. 22.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 15 days (d) 8 days
23. 23.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 4 days (d) 5 days
24. 24.If 5 mangoes cost ₹70, how much do 3 mangoes cost? (a) ₹42 (b) ₹68 (c) ₹56 (d) ₹210
25. 25.If 5 pens cost ₹120, how much do 9 pens cost? (a) ₹124 (b) ₹216 (c) ₹240 (d) ₹1080
26. 26.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 13 days
27. 27.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹76 (b) ₹133 (c) ₹19 (d) ₹152
28. 28.If 8 pens cost ₹152, how much do 6 pens cost? (a) ₹912 (b) ₹133 (c) ₹150 (d) ₹114
29. 29.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹38 (b) ₹19 (c) ₹76 (d) ₹57
30. 30.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 15 days
31. 31.If 9 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹40 (b) ₹25 (c) ₹20 (d) ₹180
32. 32.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹490 (b) ₹441 (c) ₹49 (d) ₹98
33. 33.If 6 mangoes cost ₹66, how much do 11 mangoes cost? (a) ₹121 (b) ₹71 (c) ₹132 (d) ₹726
34. 34.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 6 days (d) 7 days
35. 35.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days
36. 36.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 1 day (d) 37 days
37. 37.If 3 mangoes cost ₹57, how much do 2 mangoes cost? (a) ₹38 (b) ₹56 (c) ₹114 (d) ₹57
38. 38.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 8 days (d) 6 days
39. 39.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹66 (b) ₹55 (c) ₹77 (d) ₹11
40. 40.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 18 days (d) 19 days

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