Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 935 · 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.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹5 (c) ₹10 (d) ₹45
2. 2.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹195 (b) ₹273 (c) ₹39 (d) ₹351
3. 3.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹40 (b) ₹120 (c) ₹60 (d) ₹80
4. 4.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 13 days
5. 5.If 4 kites cost ₹100, how much do 6 kites cost? (a) ₹600 (b) ₹175 (c) ₹102 (d) ₹150
6. 6.If 2 notebooks cost ₹14, how much do 4 notebooks cost? (a) ₹56 (b) ₹28 (c) ₹16 (d) ₹35
7. 7.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 5 days (d) 8 days
8. 8.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 1 day (d) 2 days
9. 9.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 13 days (d) 11 days
10. 10.If 4 pens cost ₹72, how much do 8 pens cost? (a) ₹76 (b) ₹162 (c) ₹144 (d) ₹576
11. 11.If 9 pens cost ₹90, how much do 10 pens cost? (a) ₹100 (b) ₹900 (c) ₹91 (d) ₹110
12. 12.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 12 days (d) 7 days
13. 13.If 2 mangoes cost ₹42, how much do 6 mangoes cost? (a) ₹46 (b) ₹147 (c) ₹252 (d) ₹126
14. 14.If 5 mangoes cost ₹110, how much do 2 mangoes cost? (a) ₹44 (b) ₹220 (c) ₹107 (d) ₹66
15. 15.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 49 days (d) 4 days
16. 16.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 1 day (d) 37 days
17. 17.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 60 days (c) 9 days (d) 61 days
18. 18.If 8 kites cost ₹96, how much do 11 kites cost? (a) ₹99 (b) ₹1056 (c) ₹132 (d) ₹144
19. 19.If 7 mangoes cost ₹77, how much do 6 mangoes cost? (a) ₹76 (b) ₹77 (c) ₹462 (d) ₹66
20. 20.If 8 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹240 (b) ₹26 (c) ₹30 (d) ₹33
21. 21.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 43 days (c) 42 days (d) 18 days
22. 22.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹144 (b) ₹48 (c) ₹288 (d) ₹240
23. 23.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 22 days (d) 21 days
24. 24.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹48 (c) ₹8 (d) ₹56
25. 25.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 36 days (c) 5 days (d) 4 days
26. 26.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹114 (d) ₹95
27. 27.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹196 (d) ₹147
28. 28.If 3 kites cost ₹60, how much do 4 kites cost? (a) ₹240 (b) ₹100 (c) ₹61 (d) ₹80
29. 29.If 6 mangoes cost ₹30, how much do 7 mangoes cost? (a) ₹40 (b) ₹35 (c) ₹210 (d) ₹31
30. 30.₹352 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹176 (b) ₹256 (c) ₹32 (d) ₹96
31. 31.If 9 notebooks cost ₹198, how much do 4 notebooks cost? (a) ₹88 (b) ₹110 (c) ₹792 (d) ₹193
32. 32.If 6 pens cost ₹138, how much do 12 pens cost? (a) ₹1656 (b) ₹299 (c) ₹276 (d) ₹144
33. 33.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 13 days (d) 9 days
34. 34.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 19 days (d) 18 days
35. 35.₹140 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹140 (b) ₹112 (c) ₹70 (d) ₹28
36. 36.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹44 (b) ₹396 (c) ₹286 (d) ₹176
37. 37.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 9 days (d) 13 days
38. 38.₹341 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹93 (b) ₹279 (c) ₹31 (d) ₹248
39. 39.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹48 (c) ₹40 (d) ₹44
40. 40.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹148 (d) ₹296

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