Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 41 · 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. 1.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 10 days (d) 18 days
2. 2.If 7 pens cost ₹133, how much do 5 pens cost? (a) ₹131 (b) ₹665 (c) ₹95 (d) ₹114
3. 3.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 28 days (d) 8 days
4. 4.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹47 (b) ₹188 (c) ₹376 (d) ₹329
5. 5.If 2 pens cost ₹32, how much do 3 pens cost? (a) ₹64 (b) ₹48 (c) ₹96 (d) ₹33
6. 6.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 10 days
7. 7.₹225 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹180 (b) ₹181 (c) ₹45 (d) ₹225
8. 8.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 11 days (d) 9 days
9. 9.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹297 (b) ₹99 (c) ₹33 (d) ₹264
10. 10.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 24 days (c) 6 days (d) 18 days
11. 11.If 7 pens cost ₹168, how much do 11 pens cost? (a) ₹172 (b) ₹288 (c) ₹1848 (d) ₹264
12. 12.If 3 kites cost ₹51, how much do 4 kites cost? (a) ₹85 (b) ₹52 (c) ₹204 (d) ₹68
13. 13.If 7 mangoes cost ₹42, how much do 6 mangoes cost? (a) ₹42 (b) ₹252 (c) ₹41 (d) ₹36
14. 14.If 3 pens cost ₹60, how much do 6 pens cost? (a) ₹140 (b) ₹120 (c) ₹360 (d) ₹63
15. 15.If 8 notebooks cost ₹160, how much do 9 notebooks cost? (a) ₹180 (b) ₹1440 (c) ₹200 (d) ₹161
16. 16.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 16 days (d) 12 days
17. 17.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 1 day (d) 37 days
18. 18.If 3 mangoes cost ₹39, how much do 7 mangoes cost? (a) ₹273 (b) ₹104 (c) ₹91 (d) ₹43
19. 19.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹20 (b) ₹130 (c) ₹160 (d) ₹100
20. 20.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 10 days (d) 16 days
21. 21.If 8 kites cost ₹160, how much do 12 kites cost? (a) ₹1920 (b) ₹260 (c) ₹240 (d) ₹164
22. 22.If 6 notebooks cost ₹132, how much do 5 notebooks cost? (a) ₹131 (b) ₹132 (c) ₹660 (d) ₹110
23. 23.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 8 days (d) 7 days
24. 24.If 5 mangoes cost ₹65, how much do 6 mangoes cost? (a) ₹66 (b) ₹91 (c) ₹78 (d) ₹390
25. 25.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 14 days (d) 15 days
26. 26.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹99 (b) ₹132 (c) ₹165 (d) ₹33
27. 27.If 9 pens cost ₹63, how much do 12 pens cost? (a) ₹91 (b) ₹756 (c) ₹84 (d) ₹66
28. 28.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹119 (b) ₹17 (c) ₹85 (d) ₹153
29. 29.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹123 (b) ₹41 (c) ₹205 (d) ₹164
30. 30.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 45 days (d) 5 days
31. 31.₹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
32. 32.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 17 days (d) 13 days
33. 33.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
34. 34.If 4 pens cost ₹36, how much do 8 pens cost? (a) ₹288 (b) ₹72 (c) ₹81 (d) ₹40
35. 35.If 3 mangoes cost ₹39, how much do 2 mangoes cost? (a) ₹26 (b) ₹39 (c) ₹38 (d) ₹78
36. 36.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹10 (c) ₹70 (d) ₹50
37. 37.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹39 (b) ₹13 (c) ₹26 (d) ₹52
38. 38.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹180 (b) ₹72 (c) ₹36 (d) ₹126
39. 39.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹60 (b) ₹15 (c) ₹75 (d) ₹90
40. 40.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 2 days (d) 3 days

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