Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 59 · 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 7 kites cost ₹84, how much do 8 kites cost? (a) ₹85 (b) ₹108 (c) ₹96 (d) ₹672
2. 2.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹39 (d) ₹27
3. 3.If 8 mangoes cost ₹64, how much do 6 mangoes cost? (a) ₹62 (b) ₹384 (c) ₹48 (d) ₹56
4. 4.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹48 (b) ₹8 (c) ₹56 (d) ₹40
5. 5.If 7 kites cost ₹28, how much do 6 kites cost? (a) ₹24 (b) ₹28 (c) ₹27 (d) ₹168
6. 6.If 4 pens cost ₹96, how much do 11 pens cost? (a) ₹1056 (b) ₹103 (c) ₹264 (d) ₹288
7. 7.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹65 (d) ₹78
8. 8.If 5 notebooks cost ₹65, how much do 6 notebooks cost? (a) ₹91 (b) ₹390 (c) ₹66 (d) ₹78
9. 9.If 5 pens cost ₹20, how much do 9 pens cost? (a) ₹24 (b) ₹180 (c) ₹40 (d) ₹36
10. 10.If 2 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹120 (b) ₹32 (c) ₹60 (d) ₹75
11. 11.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 7 days (d) 8 days
12. 12.If 9 mangoes cost ₹135, how much do 11 mangoes cost? (a) ₹137 (b) ₹165 (c) ₹180 (d) ₹1485
13. 13.If 3 pens cost ₹24, how much do 5 pens cost? (a) ₹120 (b) ₹40 (c) ₹48 (d) ₹26
14. 14.If 7 pens cost ₹91, how much do 2 pens cost? (a) ₹86 (b) ₹182 (c) ₹39 (d) ₹26
15. 15.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹105 (c) ₹21 (d) ₹84
16. 16.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹50 (b) ₹300 (c) ₹150 (d) ₹250
17. 17.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 9 days (d) 8 days
18. 18.If 7 pens cost ₹42, how much do 4 pens cost? (a) ₹168 (b) ₹39 (c) ₹30 (d) ₹24
19. 19.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹28 (d) ₹21
20. 20.If 3 mangoes cost ₹39, how much do 10 mangoes cost? (a) ₹130 (b) ₹390 (c) ₹143 (d) ₹46
21. 21.If 7 mangoes cost ₹140, how much do 8 mangoes cost? (a) ₹160 (b) ₹180 (c) ₹141 (d) ₹1120
22. 22.If 8 notebooks cost ₹120, how much do 11 notebooks cost? (a) ₹1320 (b) ₹180 (c) ₹165 (d) ₹123
23. 23.If 8 kites cost ₹200, how much do 10 kites cost? (a) ₹202 (b) ₹250 (c) ₹275 (d) ₹2000
24. 24.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹100 (b) ₹80 (c) ₹60 (d) ₹20
25. 25.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 15 days (d) 16 days
26. 26.If 2 notebooks cost ₹16, how much do 8 notebooks cost? (a) ₹72 (b) ₹64 (c) ₹128 (d) ₹22
27. 27.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 21 days (c) 22 days (d) 12 days
28. 28.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹34 (b) ₹306 (c) ₹221 (d) ₹136
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
30. 30.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 8 days (d) 10 days
31. 31.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 9 days (d) 7 days
32. 32.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹80 (b) ₹112 (c) ₹96 (d) ₹16
33. 33.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 12 days (d) 4 days
34. 34.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 1 day
35. 35.If 4 mangoes cost ₹48, how much do 8 mangoes cost? (a) ₹52 (b) ₹108 (c) ₹96 (d) ₹384
36. 36.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹54 (b) ₹108 (c) ₹96 (d) ₹12
37. 37.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹20 (b) ₹25 (c) ₹60 (d) ₹16
38. 38.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 16 days (d) 14 days
39. 39.If 9 pens cost ₹144, how much do 6 pens cost? (a) ₹864 (b) ₹96 (c) ₹112 (d) ₹141
40. 40.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 20 days (d) 5 days

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