Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 190 · 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 ₹69, how much do 4 pens cost? (a) ₹276 (b) ₹115 (c) ₹70 (d) ₹92
2. 2.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹80 (b) ₹64 (c) ₹72 (d) ₹16
3. 3.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 8 days (d) 11 days
4. 4.If 2 pens cost ₹38, how much do 7 pens cost? (a) ₹152 (b) ₹133 (c) ₹43 (d) ₹266
5. 5.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 12 days
6. 6.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
7. 7.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹21 (b) ₹189 (c) ₹147 (d) ₹105
8. 8.If 6 kites cost ₹48, how much do 5 kites cost? (a) ₹48 (b) ₹240 (c) ₹40 (d) ₹47
9. 9.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 19 days (d) 7 days
10. 10.If 3 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹37 (b) ₹60 (c) ₹48 (d) ₹144
11. 11.If 9 notebooks cost ₹144, how much do 11 notebooks cost? (a) ₹1584 (b) ₹146 (c) ₹176 (d) ₹192
12. 12.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 16 days (d) 9 days
13. 13.If 6 pens cost ₹18, how much do 10 pens cost? (a) ₹180 (b) ₹30 (c) ₹33 (d) ₹22
14. 14.If 2 mangoes cost ₹34, how much do 7 mangoes cost? (a) ₹136 (b) ₹238 (c) ₹39 (d) ₹119
15. 15.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹39 (c) ₹57 (d) ₹38
16. 16.If 7 kites cost ₹161, how much do 8 kites cost? (a) ₹162 (b) ₹1288 (c) ₹207 (d) ₹184
17. 17.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 12 days
18. 18.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 31 days (d) 30 days
19. 19.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹18 (c) ₹42 (d) ₹6
20. 20.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 17 days
21. 21.If 7 pens cost ₹161, how much do 5 pens cost? (a) ₹805 (b) ₹138 (c) ₹115 (d) ₹159
22. 22.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹80 (c) ₹70 (d) ₹10
23. 23.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 11 days (d) 4 days
24. 24.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 16 days (d) 15 days
25. 25.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 5 days (d) 4 days
26. 26.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 18 days (d) 6 days
27. 27.If 4 pens cost ₹60, how much do 3 pens cost? (a) ₹60 (b) ₹180 (c) ₹45 (d) ₹59
28. 28.If 3 pens cost ₹30, how much do 12 pens cost? (a) ₹39 (b) ₹360 (c) ₹130 (d) ₹120
29. 29.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹8 (b) ₹32 (c) ₹64 (d) ₹56
30. 30.If 8 kites cost ₹192, how much do 3 kites cost? (a) ₹187 (b) ₹96 (c) ₹72 (d) ₹576
31. 31.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 2 days
32. 32.If 8 mangoes cost ₹64, how much do 6 mangoes cost? (a) ₹384 (b) ₹62 (c) ₹56 (d) ₹48
33. 33.If 8 kites cost ₹200, how much do 2 kites cost? (a) ₹75 (b) ₹50 (c) ₹400 (d) ₹194
34. 34.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 33 days (c) 32 days (d) 2 days
35. 35.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 9 days (d) 15 days
36. 36.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹30 (d) ₹40
37. 37.If 3 kites cost ₹45, how much do 11 kites cost? (a) ₹495 (b) ₹53 (c) ₹180 (d) ₹165
38. 38.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 15 days (c) 9 days (d) 22 days
39. 39.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹324 (b) ₹36 (c) ₹234 (d) ₹144
40. 40.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹238 (b) ₹136 (c) ₹34 (d) ₹187

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