Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 793 · 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.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹52 (d) ₹78
2. 2.If 7 kites cost ₹98, how much do 2 kites cost? (a) ₹28 (b) ₹196 (c) ₹42 (d) ₹93
3. 3.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 28 days (d) 27 days
4. 4.If 8 mangoes cost ₹120, how much do 5 mangoes cost? (a) ₹600 (b) ₹117 (c) ₹75 (d) ₹90
5. 5.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 11 days (d) 15 days
6. 6.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹208 (b) ₹32 (c) ₹128 (d) ₹288
7. 7.If 3 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹720 (b) ₹69 (c) ₹260 (d) ₹240
8. 8.₹140 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹105 (b) ₹140 (c) ₹70 (d) ₹35
9. 9.If 6 notebooks cost ₹60, how much do 12 notebooks cost? (a) ₹130 (b) ₹66 (c) ₹720 (d) ₹120
10. 10.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 11 days
11. 11.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 12 days (d) 11 days
12. 12.If 3 notebooks cost ₹75, how much do 11 notebooks cost? (a) ₹83 (b) ₹300 (c) ₹275 (d) ₹825
13. 13.If 3 pens cost ₹69, how much do 11 pens cost? (a) ₹759 (b) ₹77 (c) ₹276 (d) ₹253
14. 14.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 16 days (d) 15 days
15. 15.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 14 days (d) 33 days
16. 16.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 9 days
17. 17.If 4 mangoes cost ₹80, how much do 10 mangoes cost? (a) ₹220 (b) ₹200 (c) ₹800 (d) ₹86
18. 18.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 12 days (d) 7 days
19. 19.If 2 pens cost ₹6, how much do 6 pens cost? (a) ₹10 (b) ₹21 (c) ₹18 (d) ₹36
20. 20.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹28 (c) ₹8 (d) ₹32
21. 21.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 4 days
22. 22.If 3 pens cost ₹45, how much do 5 pens cost? (a) ₹90 (b) ₹225 (c) ₹47 (d) ₹75
23. 23.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹143 (b) ₹26 (c) ₹78 (d) ₹208
24. 24.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹282 (d) ₹235
25. 25.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹112 (b) ₹48 (c) ₹16 (d) ₹80
26. 26.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 15 days (d) 6 days
27. 27.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹37 (b) ₹74 (c) ₹259 (d) ₹296
28. 28.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹90 (d) ₹135
29. 29.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 16 days (d) 36 days
30. 30.If 8 notebooks cost ₹104, how much do 7 notebooks cost? (a) ₹104 (b) ₹103 (c) ₹728 (d) ₹91
31. 31.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 3 days
32. 32.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 10 days (d) 7 days
33. 33.If 5 notebooks cost ₹90, how much do 10 notebooks cost? (a) ₹95 (b) ₹198 (c) ₹180 (d) ₹900
34. 34.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 5 days (d) 20 days
35. 35.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 19 days
36. 36.If 3 kites cost ₹63, how much do 12 kites cost? (a) ₹252 (b) ₹273 (c) ₹756 (d) ₹72
37. 37.If 2 mangoes cost ₹8, how much do 7 mangoes cost? (a) ₹13 (b) ₹28 (c) ₹32 (d) ₹56
38. 38.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 15 days (d) 9 days
39. 39.If 2 pens cost ₹32, how much do 4 pens cost? (a) ₹80 (b) ₹34 (c) ₹128 (d) ₹64
40. 40.₹324 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹36 (b) ₹162 (c) ₹72 (d) ₹252

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