Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 958 · 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. 1.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 16 days (d) 11 days
2. 2.If 7 pens cost ₹35, how much do 2 pens cost? (a) ₹70 (b) ₹15 (c) ₹10 (d) ₹30
3. 3.₹405 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹360 (d) ₹361
4. 4.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 10 days (c) 14 days (d) 20 days
5. 5.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 21 days (c) 22 days (d) 13 days
6. 6.If 9 notebooks cost ₹198, how much do 10 notebooks cost? (a) ₹1980 (b) ₹242 (c) ₹199 (d) ₹220
7. 7.If 6 pens cost ₹24, how much do 2 pens cost? (a) ₹48 (b) ₹20 (c) ₹8 (d) ₹12
8. 8.If 7 kites cost ₹161, how much do 4 kites cost? (a) ₹158 (b) ₹644 (c) ₹115 (d) ₹92
9. 9.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹190 (b) ₹228 (c) ₹38 (d) ₹266
10. 10.If 2 pens cost ₹22, how much do 12 pens cost? (a) ₹132 (b) ₹143 (c) ₹264 (d) ₹32
11. 11.If 3 kites cost ₹30, how much do 5 kites cost? (a) ₹60 (b) ₹150 (c) ₹32 (d) ₹50
12. 12.₹192 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹96 (b) ₹192 (c) ₹168 (d) ₹24
13. 13.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
14. 14.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹92 (d) ₹69
15. 15.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹22 (b) ₹176 (c) ₹110 (d) ₹143
16. 16.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 15 days (d) 16 days
17. 17.If 2 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹360 (b) ₹180 (c) ₹200 (d) ₹47
18. 18.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹200 (d) ₹225
19. 19.If 9 pens cost ₹117, how much do 10 pens cost? (a) ₹143 (b) ₹1170 (c) ₹130 (d) ₹118
20. 20.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 1 day (d) 2 days
21. 21.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹196 (d) ₹168
22. 22.8 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) 33 days (d) 14 days
23. 23.If 2 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹31 (b) ₹84 (c) ₹70 (d) ₹140
24. 24.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹150 (d) ₹250
25. 25.If 8 kites cost ₹32, how much do 10 kites cost? (a) ₹40 (b) ₹320 (c) ₹34 (d) ₹44
26. 26.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 33 days (d) 5 days
27. 27.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹126 (d) ₹180
28. 28.If 7 notebooks cost ₹161, how much do 4 notebooks cost? (a) ₹644 (b) ₹115 (c) ₹158 (d) ₹92
29. 29.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹77 (b) ₹70 (c) ₹14 (d) ₹84
30. 30.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 12 days (d) 3 days
31. 31.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹5 (d) ₹30
32. 32.If 2 notebooks cost ₹50, how much do 12 notebooks cost? (a) ₹600 (b) ₹300 (c) ₹60 (d) ₹325
33. 33.If 7 mangoes cost ₹140, how much do 12 mangoes cost? (a) ₹145 (b) ₹240 (c) ₹260 (d) ₹1680
34. 34.If 9 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹18 (b) ₹162 (c) ₹24 (d) ₹48
35. 35.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹5 (d) ₹45
36. 36.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹18 (b) ₹108 (c) ₹126 (d) ₹63
37. 37.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 6 days (d) 9 days
38. 38.If 2 notebooks cost ₹30, how much do 6 notebooks cost? (a) ₹90 (b) ₹180 (c) ₹34 (d) ₹105
39. 39.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 8 days (d) 9 days
40. 40.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹63 (b) ₹189 (c) ₹168 (d) ₹21

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