Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 984 · 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. 1.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 22 days (d) 21 days
2. 2.If 4 mangoes cost ₹92, how much do 5 mangoes cost? (a) ₹138 (b) ₹93 (c) ₹115 (d) ₹460
3. 3.₹100 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹100 (c) ₹20 (d) ₹50
4. 4.If 2 mangoes cost ₹20, how much do 4 mangoes cost? (a) ₹22 (b) ₹50 (c) ₹40 (d) ₹80
5. 5.If 5 pens cost ₹60, how much do 10 pens cost? (a) ₹65 (b) ₹120 (c) ₹600 (d) ₹132
6. 6.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹105 (c) ₹21 (d) ₹63
7. 7.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 19 days (d) 3 days
8. 8.If 5 notebooks cost ₹40, how much do 2 notebooks cost? (a) ₹24 (b) ₹37 (c) ₹80 (d) ₹16
9. 9.If 5 notebooks cost ₹115, how much do 3 notebooks cost? (a) ₹113 (b) ₹69 (c) ₹92 (d) ₹345
10. 10.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 11 days (d) 45 days
11. 11.If 7 pens cost ₹77, how much do 8 pens cost? (a) ₹616 (b) ₹88 (c) ₹78 (d) ₹99
12. 12.If 2 notebooks cost ₹6, how much do 12 notebooks cost? (a) ₹72 (b) ₹36 (c) ₹16 (d) ₹39
13. 13.If 9 kites cost ₹144, how much do 11 kites cost? (a) ₹176 (b) ₹146 (c) ₹1584 (d) ₹192
14. 14.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 23 days (d) 12 days
15. 15.If 3 pens cost ₹48, how much do 11 pens cost? (a) ₹56 (b) ₹528 (c) ₹176 (d) ₹192
16. 16.If 8 notebooks cost ₹72, how much do 10 notebooks cost? (a) ₹720 (b) ₹74 (c) ₹99 (d) ₹90
17. 17.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 19 days (d) 11 days
18. 18.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 28 days (c) 7 days (d) 18 days
19. 19.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 14 days (d) 15 days
20. 20.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹56 (c) ₹8 (d) ₹48
21. 21.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 25 days (d) 4 days
22. 22.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 16 days (c) 8 days (d) 4 days
23. 23.If 8 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹864 (b) ₹76 (c) ₹108 (d) ₹117
24. 24.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 36 days (d) 17 days
25. 25.If 2 kites cost ₹44, how much do 11 kites cost? (a) ₹484 (b) ₹53 (c) ₹264 (d) ₹242
26. 26.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 6 days (d) 36 days
27. 27.If 4 kites cost ₹24, how much do 7 kites cost? (a) ₹27 (b) ₹42 (c) ₹48 (d) ₹168
28. 28.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 22 days (d) 13 days
29. 29.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹78 (b) ₹91 (c) ₹13 (d) ₹79
30. 30.If 3 notebooks cost ₹9, how much do 2 notebooks cost? (a) ₹8 (b) ₹18 (c) ₹6 (d) ₹9
31. 31.If 3 mangoes cost ₹39, how much do 12 mangoes cost? (a) ₹169 (b) ₹156 (c) ₹48 (d) ₹468
32. 32.If 6 pens cost ₹60, how much do 5 pens cost? (a) ₹300 (b) ₹50 (c) ₹60 (d) ₹59
33. 33.If 5 mangoes cost ₹125, how much do 6 mangoes cost? (a) ₹126 (b) ₹750 (c) ₹175 (d) ₹150
34. 34.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹55 (c) ₹66 (d) ₹11
35. 35.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹180 (d) ₹165
36. 36.If 5 kites cost ₹35, how much do 4 kites cost? (a) ₹35 (b) ₹28 (c) ₹140 (d) ₹34
37. 37.₹220 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹22 (b) ₹220 (c) ₹198 (d) ₹110
38. 38.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 4 days (d) 3 days
39. 39.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹85 (b) ₹102 (c) ₹68 (d) ₹34
40. 40.If 6 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹288 (b) ₹70 (c) ₹60 (d) ₹48

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