Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 729 · 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.If 6 pens cost ₹126, how much do 4 pens cost? (a) ₹84 (b) ₹105 (c) ₹124 (d) ₹504
2. 2.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹248 (d) ₹124
3. 3.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 6 days (c) 4 days (d) 18 days
4. 4.If 3 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹80 (b) ₹49 (c) ₹64 (d) ₹192
5. 5.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹84 (d) ₹42
6. 6.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 7 days
7. 7.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹215 (d) ₹344
8. 8.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹252 (d) ₹294
9. 9.If 9 kites cost ₹36, how much do 12 kites cost? (a) ₹39 (b) ₹52 (c) ₹48 (d) ₹432
10. 10.₹72 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹72 (d) ₹54
11. 11.If 5 mangoes cost ₹120, how much do 6 mangoes cost? (a) ₹720 (b) ₹168 (c) ₹144 (d) ₹121
12. 12.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹322 (b) ₹368 (c) ₹46 (d) ₹184
13. 13.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 13 days (d) 12 days
14. 14.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 17 days (d) 11 days
15. 15.If 7 kites cost ₹49, how much do 12 kites cost? (a) ₹84 (b) ₹91 (c) ₹588 (d) ₹54
16. 16.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 49 days (d) 19 days
17. 17.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 21 days (d) 9 days
18. 18.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
19. 19.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 19 days (d) 18 days
20. 20.If 8 mangoes cost ₹80, how much do 7 mangoes cost? (a) ₹560 (b) ₹79 (c) ₹70 (d) ₹80
21. 21.If 2 kites cost ₹50, how much do 10 kites cost? (a) ₹500 (b) ₹58 (c) ₹250 (d) ₹275
22. 22.5 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) 9 days (d) 6 days
23. 23.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 14 days (c) 8 days (d) 15 days
24. 24.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹108 (c) ₹12 (d) ₹60
25. 25.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹33 (d) ₹44
26. 26.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 8 days (d) 7 days
27. 27.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 9 days (d) 18 days
28. 28.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹48 (d) ₹30
29. 29.If 8 kites cost ₹80, how much do 7 kites cost? (a) ₹70 (b) ₹80 (c) ₹560 (d) ₹79
30. 30.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 17 days (d) 9 days
31. 31.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 11 days (d) 10 days
32. 32.If 2 pens cost ₹16, how much do 11 pens cost? (a) ₹25 (b) ₹176 (c) ₹88 (d) ₹96
33. 33.If 2 pens cost ₹46, how much do 3 pens cost? (a) ₹47 (b) ₹138 (c) ₹69 (d) ₹92
34. 34.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 3 days (d) 4 days
35. 35.If 4 notebooks cost ₹52, how much do 10 notebooks cost? (a) ₹520 (b) ₹143 (c) ₹58 (d) ₹130
36. 36.If 9 mangoes cost ₹207, how much do 5 mangoes cost? (a) ₹138 (b) ₹1035 (c) ₹115 (d) ₹203
37. 37.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
38. 38.If 9 notebooks cost ₹171, how much do 5 notebooks cost? (a) ₹855 (b) ₹114 (c) ₹95 (d) ₹167
39. 39.If 6 kites cost ₹90, how much do 7 kites cost? (a) ₹630 (b) ₹105 (c) ₹91 (d) ₹120
40. 40.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹312 (b) ₹432 (c) ₹192 (d) ₹48

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