Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 231 · 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 notebooks cost ₹150, how much do 10 notebooks cost? (a) ₹154 (b) ₹250 (c) ₹1500 (d) ₹275
2. 2.If 2 pens cost ₹18, how much do 5 pens cost? (a) ₹90 (b) ₹21 (c) ₹45 (d) ₹54
3. 3.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 13 days (d) 11 days
4. 4.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹60 (b) ₹80 (c) ₹40 (d) ₹20
5. 5.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 10 days (d) 3 days
6. 6.If 3 pens cost ₹72, how much do 10 pens cost? (a) ₹79 (b) ₹264 (c) ₹240 (d) ₹720
7. 7.If 3 kites cost ₹9, how much do 4 kites cost? (a) ₹15 (b) ₹36 (c) ₹12 (d) ₹10
8. 8.If 9 pens cost ₹27, how much do 10 pens cost? (a) ₹33 (b) ₹28 (c) ₹30 (d) ₹270
9. 9.If 9 mangoes cost ₹126, how much do 7 mangoes cost? (a) ₹124 (b) ₹882 (c) ₹112 (d) ₹98
10. 10.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 3 days (d) 5 days
11. 11.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹234 (b) ₹36 (c) ₹288 (d) ₹180
12. 12.If 6 pens cost ₹120, how much do 3 pens cost? (a) ₹60 (b) ₹360 (c) ₹80 (d) ₹117
13. 13.If 9 pens cost ₹144, how much do 7 pens cost? (a) ₹142 (b) ₹1008 (c) ₹128 (d) ₹112
14. 14.If 5 pens cost ₹45, how much do 9 pens cost? (a) ₹405 (b) ₹49 (c) ₹81 (d) ₹90
15. 15.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 1 day (d) 11 days
16. 16.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹150 (b) ₹120 (c) ₹75 (d) ₹30
17. 17.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹68
18. 18.If 3 mangoes cost ₹30, how much do 11 mangoes cost? (a) ₹120 (b) ₹38 (c) ₹330 (d) ₹110
19. 19.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 6 days
20. 20.If 9 pens cost ₹63, how much do 10 pens cost? (a) ₹70 (b) ₹77 (c) ₹64 (d) ₹630
21. 21.If 9 pens cost ₹108, how much do 4 pens cost? (a) ₹432 (b) ₹103 (c) ₹60 (d) ₹48
22. 22.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 12 days (d) 7 days
23. 23.If 5 pens cost ₹105, how much do 3 pens cost? (a) ₹84 (b) ₹63 (c) ₹103 (d) ₹315
24. 24.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹12 (c) ₹18 (d) ₹6
25. 25.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹240 (c) ₹40 (d) ₹280
26. 26.If 3 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹14 (b) ₹20 (c) ₹60 (d) ₹24
27. 27.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹126 (c) ₹162 (d) ₹18
28. 28.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹26 (d) ₹78
29. 29.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹50 (b) ₹75 (c) ₹100 (d) ₹25
30. 30.If 6 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹32 (b) ₹18 (c) ₹12 (d) ₹72
31. 31.If 4 pens cost ₹84, how much do 12 pens cost? (a) ₹252 (b) ₹1008 (c) ₹273 (d) ₹92
32. 32.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 7 days (d) 52 days
33. 33.If 6 mangoes cost ₹90, how much do 5 mangoes cost? (a) ₹89 (b) ₹90 (c) ₹75 (d) ₹450
34. 34.If 7 notebooks cost ₹21, how much do 10 notebooks cost? (a) ₹33 (b) ₹30 (c) ₹24 (d) ₹210
35. 35.If 3 pens cost ₹54, how much do 10 pens cost? (a) ₹180 (b) ₹61 (c) ₹198 (d) ₹540
36. 36.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 13 days (d) 12 days
37. 37.If 6 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹252 (b) ₹42 (c) ₹48 (d) ₹37
38. 38.If 3 notebooks cost ₹69, how much do 4 notebooks cost? (a) ₹276 (b) ₹115 (c) ₹92 (d) ₹70
39. 39.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 28 days (d) 27 days
40. 40.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹5 (d) ₹35

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