Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 139 · 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.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹200 (b) ₹350 (c) ₹275 (d) ₹50
2. 2.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹195 (d) ₹117
3. 3.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹31 (b) ₹93 (c) ₹124 (d) ₹155
4. 4.₹105 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹90 (d) ₹91
5. 5.If 4 kites cost ₹100, how much do 11 kites cost? (a) ₹107 (b) ₹1100 (c) ₹275 (d) ₹300
6. 6.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹48 (d) ₹44
7. 7.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹242 (d) ₹264
8. 8.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹45 (c) ₹15 (d) ₹31
9. 9.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹24 (b) ₹168 (c) ₹132 (d) ₹96
10. 10.If 2 kites cost ₹30, how much do 7 kites cost? (a) ₹210 (b) ₹120 (c) ₹35 (d) ₹105
11. 11.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 1 day (d) 17 days
12. 12.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹56 (b) ₹112 (c) ₹16 (d) ₹96
13. 13.If 4 kites cost ₹16, how much do 10 kites cost? (a) ₹160 (b) ₹22 (c) ₹40 (d) ₹44
14. 14.If 9 notebooks cost ₹153, how much do 5 notebooks cost? (a) ₹765 (b) ₹102 (c) ₹149 (d) ₹85
15. 15.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
16. 16.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹119
17. 17.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 10 days (d) 11 days
18. 18.If 9 kites cost ₹63, how much do 3 kites cost? (a) ₹189 (b) ₹57 (c) ₹21 (d) ₹28
19. 19.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹60 (d) ₹45
20. 20.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 2 days (c) 3 days (d) 4 days
21. 21.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
22. 22.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 18 days (d) 6 days
23. 23.If 3 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹40 (b) ₹32 (c) ₹25 (d) ₹96
24. 24.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹22 (b) ₹55 (c) ₹88 (d) ₹110
25. 25.If 9 pens cost ₹54, how much do 6 pens cost? (a) ₹324 (b) ₹42 (c) ₹51 (d) ₹36
26. 26.If 4 notebooks cost ₹44, how much do 11 notebooks cost? (a) ₹51 (b) ₹121 (c) ₹484 (d) ₹132
27. 27.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹114 (b) ₹38 (c) ₹133 (d) ₹152
28. 28.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 7 days (d) 6 days
29. 29.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹324 (c) ₹180 (d) ₹36
30. 30.If 2 mangoes cost ₹46, how much do 6 mangoes cost? (a) ₹161 (b) ₹138 (c) ₹276 (d) ₹50
31. 31.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹20 (c) ₹180 (d) ₹160
32. 32.If 8 pens cost ₹136, how much do 9 pens cost? (a) ₹1224 (b) ₹153 (c) ₹170 (d) ₹137
33. 33.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 22 days (d) 21 days
34. 34.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹370 (b) ₹37 (c) ₹148 (d) ₹333
35. 35.If 5 notebooks cost ₹115, how much do 2 notebooks cost? (a) ₹112 (b) ₹230 (c) ₹69 (d) ₹46
36. 36.If 7 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹18 (b) ₹84 (c) ₹15 (d) ₹12
37. 37.If 8 pens cost ₹200, how much do 9 pens cost? (a) ₹201 (b) ₹1800 (c) ₹250 (d) ₹225
38. 38.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 11 days
39. 39.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 4 days (d) 3 days
40. 40.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 2 days (c) 4 days (d) 3 days

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