Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 323 · 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 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 10 days (d) 18 days
2. 2.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 2 days (d) 12 days
3. 3.If 3 pens cost ₹42, how much do 6 pens cost? (a) ₹252 (b) ₹84 (c) ₹45 (d) ₹98
4. 4.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 17 days
5. 5.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 52 days (c) 53 days (d) 7 days
6. 6.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 3 days (d) 27 days
7. 7.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹16 (b) ₹48 (c) ₹64 (d) ₹56
8. 8.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 20 days (d) 13 days
9. 9.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 3 days (d) 12 days
10. 10.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 6 days (d) 5 days
11. 11.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 54 days (c) 55 days (d) 5 days
12. 12.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 28 days (c) 7 days (d) 18 days
13. 13.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹222 (b) ₹37 (c) ₹223 (d) ₹259
14. 14.If 2 pens cost ₹18, how much do 4 pens cost? (a) ₹20 (b) ₹72 (c) ₹45 (d) ₹36
15. 15.If 7 pens cost ₹28, how much do 2 pens cost? (a) ₹8 (b) ₹23 (c) ₹56 (d) ₹12
16. 16.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 1 day (d) 9 days
17. 17.₹126 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹98 (b) ₹28 (c) ₹14 (d) ₹63
18. 18.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹15 (b) ₹25 (c) ₹35 (d) ₹5
19. 19.If 7 kites cost ₹28, how much do 12 kites cost? (a) ₹33 (b) ₹52 (c) ₹48 (d) ₹336
20. 20.If 9 mangoes cost ₹90, how much do 8 mangoes cost? (a) ₹720 (b) ₹90 (c) ₹80 (d) ₹89
21. 21.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹34 (b) ₹119 (c) ₹204 (d) ₹238
22. 22.If 4 pens cost ₹56, how much do 7 pens cost? (a) ₹59 (b) ₹98 (c) ₹392 (d) ₹112
23. 23.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹180 (d) ₹144
24. 24.₹369 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹246 (b) ₹41 (c) ₹164 (d) ₹205
25. 25.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹46 (d) ₹161
26. 26.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹76 (d) ₹95
27. 27.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 11 days (d) 5 days
28. 28.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹261 (d) ₹145
29. 29.If 3 notebooks cost ₹66, how much do 7 notebooks cost? (a) ₹70 (b) ₹154 (c) ₹462 (d) ₹176
30. 30.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹112 (b) ₹56 (c) ₹14 (d) ₹98
31. 31.If 7 pens cost ₹105, how much do 10 pens cost? (a) ₹1050 (b) ₹108 (c) ₹165 (d) ₹150
32. 32.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
33. 33.If 3 mangoes cost ₹30, how much do 10 mangoes cost? (a) ₹37 (b) ₹300 (c) ₹110 (d) ₹100
34. 34.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 21 days (d) 1 day
35. 35.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 2 days (d) 7 days
36. 36.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 14 days (d) 2 days
37. 37.If 2 kites cost ₹10, how much do 11 kites cost? (a) ₹55 (b) ₹110 (c) ₹60 (d) ₹19
38. 38.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 8 days (c) 4 days (d) 16 days
39. 39.If 9 kites cost ₹216, how much do 6 kites cost? (a) ₹213 (b) ₹168 (c) ₹144 (d) ₹1296
40. 40.If 2 notebooks cost ₹10, how much do 11 notebooks cost? (a) ₹60 (b) ₹110 (c) ₹19 (d) ₹55

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