Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 579 · 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 3 notebooks cost ₹66, how much do 4 notebooks cost? (a) ₹264 (b) ₹88 (c) ₹67 (d) ₹110
2. 2.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹13 (b) ₹104 (c) ₹65 (d) ₹117
3. 3.If 9 kites cost ₹162, how much do 7 kites cost? (a) ₹126 (b) ₹144 (c) ₹1134 (d) ₹160
4. 4.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 15 days (d) 27 days
5. 5.If 6 mangoes cost ₹48, how much do 3 mangoes cost? (a) ₹45 (b) ₹24 (c) ₹32 (d) ₹144
6. 6.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹55 (c) ₹10 (d) ₹60
7. 7.If 5 notebooks cost ₹20, how much do 6 notebooks cost? (a) ₹28 (b) ₹21 (c) ₹24 (d) ₹120
8. 8.If 3 kites cost ₹54, how much do 4 kites cost? (a) ₹90 (b) ₹216 (c) ₹72 (d) ₹55
9. 9.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 13 days (d) 9 days
10. 10.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹39 (d) ₹13
11. 11.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 4 days (d) 3 days
12. 12.If 6 kites cost ₹36, how much do 3 kites cost? (a) ₹24 (b) ₹108 (c) ₹33 (d) ₹18
13. 13.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹33 (d) ₹36
14. 14.₹495 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹450 (b) ₹90 (c) ₹45 (d) ₹405
15. 15.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 6 days (d) 24 days
16. 16.If 9 kites cost ₹144, how much do 6 kites cost? (a) ₹96 (b) ₹864 (c) ₹112 (d) ₹141
17. 17.If 8 pens cost ₹200, how much do 2 pens cost? (a) ₹50 (b) ₹400 (c) ₹75 (d) ₹194
18. 18.If 4 mangoes cost ₹16, how much do 10 mangoes cost? (a) ₹40 (b) ₹44 (c) ₹22 (d) ₹160
19. 19.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 17 days (d) 21 days
20. 20.If 2 kites cost ₹40, how much do 4 kites cost? (a) ₹100 (b) ₹160 (c) ₹80 (d) ₹42
21. 21.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 15 days (d) 14 days
22. 22.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹90 (d) ₹75
23. 23.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
24. 24.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 14 days (d) 2 days
25. 25.₹92 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹46 (d) ₹69
26. 26.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹35 (c) ₹28 (d) ₹7
27. 27.9 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) 8 days (d) 5 days
28. 28.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹32 (d) ₹40
29. 29.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹57 (b) ₹38 (c) ₹76 (d) ₹19
30. 30.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 1 day
31. 31.If 5 pens cost ₹35, how much do 4 pens cost? (a) ₹140 (b) ₹34 (c) ₹28 (d) ₹35
32. 32.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹90 (b) ₹126 (c) ₹54 (d) ₹18
33. 33.If 9 notebooks cost ₹180, how much do 5 notebooks cost? (a) ₹120 (b) ₹100 (c) ₹900 (d) ₹176
34. 34.If 6 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹27 (b) ₹40 (c) ₹36 (d) ₹216
35. 35.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
36. 36.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 13 days (d) 7 days
37. 37.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 7 days
38. 38.If 3 mangoes cost ₹18, how much do 10 mangoes cost? (a) ₹180 (b) ₹66 (c) ₹25 (d) ₹60
39. 39.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹430 (b) ₹387 (c) ₹86 (d) ₹43
40. 40.If 7 notebooks cost ₹21, how much do 3 notebooks cost? (a) ₹12 (b) ₹63 (c) ₹9 (d) ₹17

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