Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 43 · 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 pens cost ₹27, how much do 4 pens cost? (a) ₹36 (b) ₹108 (c) ₹28 (d) ₹45
2. 2.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 13 days (d) 9 days
3. 3.If 4 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹30 (b) ₹80 (c) ₹20 (d) ₹38
4. 4.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹245 (b) ₹147 (c) ₹196 (d) ₹49
5. 5.₹189 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹54 (d) ₹27
6. 6.If 4 pens cost ₹44, how much do 3 pens cost? (a) ₹44 (b) ₹33 (c) ₹132 (d) ₹43
7. 7.If 3 kites cost ₹18, how much do 12 kites cost? (a) ₹72 (b) ₹78 (c) ₹27 (d) ₹216
8. 8.If 4 kites cost ₹76, how much do 3 kites cost? (a) ₹75 (b) ₹228 (c) ₹76 (d) ₹57
9. 9.₹220 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹22 (b) ₹198 (c) ₹220 (d) ₹110
10. 10.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹192 (c) ₹24 (d) ₹156
11. 11.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 18 days (d) 12 days
12. 12.If 6 pens cost ₹36, how much do 3 pens cost? (a) ₹24 (b) ₹18 (c) ₹108 (d) ₹33
13. 13.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 5 days
14. 14.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹75 (b) ₹150 (c) ₹100 (d) ₹50
15. 15.If 8 pens cost ₹24, how much do 7 pens cost? (a) ₹21 (b) ₹23 (c) ₹24 (d) ₹168
16. 16.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 7 days
17. 17.3 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
18. 18.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 6 days
19. 19.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹72 (b) ₹96 (c) ₹24 (d) ₹84
20. 20.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 15 days
21. 21.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 6 days
22. 22.If 6 notebooks cost ₹150, how much do 11 notebooks cost? (a) ₹1650 (b) ₹300 (c) ₹155 (d) ₹275
23. 23.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹28 (c) ₹56 (d) ₹42
24. 24.If 9 pens cost ₹72, how much do 2 pens cost? (a) ₹24 (b) ₹144 (c) ₹16 (d) ₹65
25. 25.If 2 notebooks cost ₹48, how much do 8 notebooks cost? (a) ₹54 (b) ₹192 (c) ₹216 (d) ₹384
26. 26.If 7 mangoes cost ₹28, how much do 6 mangoes cost? (a) ₹168 (b) ₹24 (c) ₹28 (d) ₹27
27. 27.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹125 (b) ₹75 (c) ₹25 (d) ₹100
28. 28.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹208 (b) ₹26 (c) ₹104 (d) ₹182
29. 29.If 3 mangoes cost ₹63, how much do 5 mangoes cost? (a) ₹315 (b) ₹65 (c) ₹126 (d) ₹105
30. 30.₹376 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹376 (b) ₹47 (c) ₹188 (d) ₹329
31. 31.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 56 days (c) 57 days (d) 20 days
32. 32.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹52 (b) ₹39 (c) ₹26 (d) ₹78
33. 33.If 9 pens cost ₹45, how much do 12 pens cost? (a) ₹48 (b) ₹60 (c) ₹65 (d) ₹540
34. 34.If 5 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹41 (b) ₹56 (c) ₹48 (d) ₹240
35. 35.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 13 days (d) 22 days
36. 36.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹48 (b) ₹120 (c) ₹24 (d) ₹84
37. 37.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹35 (c) ₹5 (d) ₹25
38. 38.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹14 (b) ₹98 (c) ₹56 (d) ₹112
39. 39.If 2 mangoes cost ₹38, how much do 10 mangoes cost? (a) ₹380 (b) ₹190 (c) ₹209 (d) ₹46
40. 40.If 6 pens cost ₹108, how much do 11 pens cost? (a) ₹113 (b) ₹1188 (c) ₹198 (d) ₹216

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