Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 312 · 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.₹105 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹84 (d) ₹85
2. 2.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 9 days (c) 40 days (d) 17 days
3. 3.₹216 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹27 (b) ₹216 (c) ₹108 (d) ₹189
4. 4.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 12 days (d) 3 days
5. 5.If 5 mangoes cost ₹35, how much do 6 mangoes cost? (a) ₹210 (b) ₹36 (c) ₹49 (d) ₹42
6. 6.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 3 days (d) 5 days
7. 7.If 2 mangoes cost ₹6, how much do 12 mangoes cost? (a) ₹72 (b) ₹16 (c) ₹39 (d) ₹36
8. 8.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 9 days (d) 7 days
9. 9.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 17 days (d) 4 days
10. 10.If 2 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹192 (b) ₹50 (c) ₹120 (d) ₹96
11. 11.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 10 days (d) 11 days
12. 12.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹10 (b) ₹90 (c) ₹20 (d) ₹55
13. 13.If 9 kites cost ₹153, how much do 3 kites cost? (a) ₹459 (b) ₹147 (c) ₹51 (d) ₹68
14. 14.If 6 kites cost ₹132, how much do 3 kites cost? (a) ₹129 (b) ₹396 (c) ₹88 (d) ₹66
15. 15.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 2 days (d) 4 days
16. 16.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹69 (c) ₹92 (d) ₹138
17. 17.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 3 days
18. 18.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 18 days (d) 12 days
19. 19.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 14 days (c) 5 days (d) 6 days
20. 20.₹170 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹51 (b) ₹85 (c) ₹17 (d) ₹119
21. 21.If 7 mangoes cost ₹21, how much do 5 mangoes cost? (a) ₹105 (b) ₹19 (c) ₹18 (d) ₹15
22. 22.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹155 (d) ₹279
23. 23.₹250 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹250 (b) ₹125 (c) ₹25 (d) ₹225
24. 24.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹174 (d) ₹145
25. 25.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 14 days
26. 26.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 2 days (d) 3 days
27. 27.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 7 days (d) 5 days
28. 28.If 7 notebooks cost ₹168, how much do 10 notebooks cost? (a) ₹1680 (b) ₹171 (c) ₹264 (d) ₹240
29. 29.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹246 (b) ₹82 (c) ₹41 (d) ₹205
30. 30.If 7 pens cost ₹105, how much do 6 pens cost? (a) ₹105 (b) ₹104 (c) ₹630 (d) ₹90
31. 31.₹350 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹175 (d) ₹300
32. 32.If 9 pens cost ₹126, how much do 8 pens cost? (a) ₹125 (b) ₹126 (c) ₹1008 (d) ₹112
33. 33.If 3 kites cost ₹36, how much do 2 kites cost? (a) ₹24 (b) ₹36 (c) ₹35 (d) ₹72
34. 34.6 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) 13 days (d) 5 days
35. 35.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹252 (b) ₹42 (c) ₹210 (d) ₹294
36. 36.If 5 kites cost ₹90, how much do 7 kites cost? (a) ₹92 (b) ₹126 (c) ₹144 (d) ₹630
37. 37.If 3 pens cost ₹69, how much do 12 pens cost? (a) ₹299 (b) ₹276 (c) ₹78 (d) ₹828
38. 38.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 36 days (d) 37 days
39. 39.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 9 days (d) 4 days
40. 40.If 4 notebooks cost ₹100, how much do 5 notebooks cost? (a) ₹150 (b) ₹101 (c) ₹500 (d) ₹125

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