Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 153 · 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 6 kites cost ₹144, how much do 10 kites cost? (a) ₹148 (b) ₹264 (c) ₹1440 (d) ₹240
2. 2.If 3 notebooks cost ₹63, how much do 5 notebooks cost? (a) ₹105 (b) ₹126 (c) ₹315 (d) ₹65
3. 3.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 8 days (d) 10 days
4. 4.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 21 days (d) 9 days
5. 5.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹119 (b) ₹85 (c) ₹17 (d) ₹153
6. 6.If 7 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹280 (b) ₹54 (c) ₹40 (d) ₹48
7. 7.If 6 mangoes cost ₹126, how much do 7 mangoes cost? (a) ₹127 (b) ₹168 (c) ₹882 (d) ₹147
8. 8.If 8 pens cost ₹48, how much do 10 pens cost? (a) ₹480 (b) ₹50 (c) ₹60 (d) ₹66
9. 9.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 13 days (d) 29 days
10. 10.If 9 pens cost ₹216, how much do 3 pens cost? (a) ₹210 (b) ₹648 (c) ₹96 (d) ₹72
11. 11.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹104 (b) ₹130 (c) ₹78 (d) ₹26
12. 12.If 5 kites cost ₹50, how much do 6 kites cost? (a) ₹60 (b) ₹51 (c) ₹300 (d) ₹70
13. 13.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 18 days (d) 12 days
14. 14.If 9 mangoes cost ₹108, how much do 7 mangoes cost? (a) ₹756 (b) ₹96 (c) ₹84 (d) ₹106
15. 15.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
16. 16.If 4 mangoes cost ₹28, how much do 11 mangoes cost? (a) ₹84 (b) ₹77 (c) ₹35 (d) ₹308
17. 17.₹252 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹252 (b) ₹210 (c) ₹126 (d) ₹42
18. 18.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹135 (c) ₹81 (d) ₹27
19. 19.If 4 kites cost ₹92, how much do 2 kites cost? (a) ₹46 (b) ₹90 (c) ₹69 (d) ₹184
20. 20.If 2 kites cost ₹22, how much do 3 kites cost? (a) ₹23 (b) ₹44 (c) ₹66 (d) ₹33
21. 21.If 5 kites cost ₹20, how much do 6 kites cost? (a) ₹120 (b) ₹21 (c) ₹24 (d) ₹28
22. 22.If 6 pens cost ₹72, how much do 7 pens cost? (a) ₹84 (b) ₹504 (c) ₹73 (d) ₹96
23. 23.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹9 (d) ₹45
24. 24.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹150 (c) ₹30 (d) ₹180
25. 25.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹28 (b) ₹224 (c) ₹154 (d) ₹84
26. 26.If 4 mangoes cost ₹96, how much do 2 mangoes cost? (a) ₹48 (b) ₹192 (c) ₹72 (d) ₹94
27. 27.If 8 notebooks cost ₹176, how much do 4 notebooks cost? (a) ₹172 (b) ₹704 (c) ₹88 (d) ₹110
28. 28.If 4 mangoes cost ₹12, how much do 7 mangoes cost? (a) ₹21 (b) ₹15 (c) ₹84 (d) ₹24
29. 29.If 8 kites cost ₹64, how much do 9 kites cost? (a) ₹72 (b) ₹80 (c) ₹65 (d) ₹576
30. 30.If 9 pens cost ₹27, how much do 4 pens cost? (a) ₹108 (b) ₹22 (c) ₹12 (d) ₹15
31. 31.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹18 (d) ₹24
32. 32.If 8 pens cost ₹24, how much do 12 pens cost? (a) ₹288 (b) ₹39 (c) ₹36 (d) ₹28
33. 33.₹150 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹75 (b) ₹150 (c) ₹125 (d) ₹25
34. 34.If 3 notebooks cost ₹45, how much do 7 notebooks cost? (a) ₹120 (b) ₹315 (c) ₹105 (d) ₹49
35. 35.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹66 (d) ₹110
36. 36.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 16 days (d) 24 days
37. 37.If 2 pens cost ₹8, how much do 10 pens cost? (a) ₹80 (b) ₹16 (c) ₹44 (d) ₹40
38. 38.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 3 days (d) 4 days
39. 39.If 3 pens cost ₹33, how much do 11 pens cost? (a) ₹41 (b) ₹132 (c) ₹121 (d) ₹363
40. 40.If 8 notebooks cost ₹32, how much do 5 notebooks cost? (a) ₹29 (b) ₹24 (c) ₹20 (d) ₹160

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