Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 107 · 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.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹72 (b) ₹8 (c) ₹44 (d) ₹16
2. 2.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹135 (b) ₹162 (c) ₹189 (d) ₹27
3. 3.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 6 days (d) 7 days
4. 4.If 8 mangoes cost ₹120, how much do 9 mangoes cost? (a) ₹1080 (b) ₹121 (c) ₹135 (d) ₹150
5. 5.If 4 mangoes cost ₹12, how much do 8 mangoes cost? (a) ₹96 (b) ₹24 (c) ₹16 (d) ₹27
6. 6.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹91 (d) ₹104
7. 7.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹65 (b) ₹117 (c) ₹13 (d) ₹130
8. 8.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 8 days (d) 2 days
9. 9.₹180 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹144 (d) ₹90
10. 10.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 4 days (d) 3 days
11. 11.₹376 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹376 (b) ₹188 (c) ₹329 (d) ₹47
12. 12.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹35 (b) ₹10 (c) ₹40 (d) ₹5
13. 13.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 3 days (d) 14 days
14. 14.If 3 pens cost ₹24, how much do 2 pens cost? (a) ₹16 (b) ₹24 (c) ₹48 (d) ₹23
15. 15.If 2 notebooks cost ₹8, how much do 7 notebooks cost? (a) ₹28 (b) ₹56 (c) ₹32 (d) ₹13
16. 16.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹25 (b) ₹15 (c) ₹5 (d) ₹20
17. 17.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 5 days (d) 6 days
18. 18.If 3 kites cost ₹66, how much do 7 kites cost? (a) ₹176 (b) ₹70 (c) ₹154 (d) ₹462
19. 19.If 3 pens cost ₹42, how much do 9 pens cost? (a) ₹140 (b) ₹378 (c) ₹48 (d) ₹126
20. 20.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹40 (c) ₹5 (d) ₹45
21. 21.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹294 (b) ₹168 (c) ₹42 (d) ₹231
22. 22.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 12 days (d) 2 days
23. 23.If 8 pens cost ₹80, how much do 5 pens cost? (a) ₹77 (b) ₹400 (c) ₹60 (d) ₹50
24. 24.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹81 (d) ₹9
25. 25.If 4 pens cost ₹96, how much do 7 pens cost? (a) ₹99 (b) ₹672 (c) ₹192 (d) ₹168
26. 26.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 18 days (d) 8 days
27. 27.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 13 days (d) 18 days
28. 28.If 5 kites cost ₹125, how much do 4 kites cost? (a) ₹100 (b) ₹125 (c) ₹500 (d) ₹124
29. 29.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 8 days (d) 9 days
30. 30.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹13 (d) ₹26
31. 31.If 8 pens cost ₹112, how much do 6 pens cost? (a) ₹84 (b) ₹98 (c) ₹110 (d) ₹672
32. 32.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹38 (b) ₹76 (c) ₹19 (d) ₹57
33. 33.If 5 notebooks cost ₹125, how much do 3 notebooks cost? (a) ₹100 (b) ₹375 (c) ₹123 (d) ₹75
34. 34.If 8 pens cost ₹40, how much do 4 pens cost? (a) ₹36 (b) ₹25 (c) ₹20 (d) ₹160
35. 35.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 6 days
36. 36.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 14 days (d) 15 days
37. 37.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 5 days (d) 13 days
38. 38.If 6 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹156 (b) ₹78 (c) ₹144 (d) ₹864
39. 39.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 17 days (c) 13 days (d) 31 days
40. 40.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 3 days

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