Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 995 · 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 notebooks cost ₹150, how much do 5 notebooks cost? (a) ₹125 (b) ₹150 (c) ₹149 (d) ₹750
2. 2.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 1 day (d) 3 days
3. 3.If 9 mangoes cost ₹108, how much do 12 mangoes cost? (a) ₹156 (b) ₹1296 (c) ₹144 (d) ₹111
4. 4.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 19 days (d) 39 days
5. 5.If 3 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹90 (b) ₹105 (c) ₹48 (d) ₹270
6. 6.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 19 days (d) 4 days
7. 7.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹234 (b) ₹195 (c) ₹117 (d) ₹39
8. 8.If 2 kites cost ₹16, how much do 6 kites cost? (a) ₹48 (b) ₹20 (c) ₹96 (d) ₹56
9. 9.If 6 kites cost ₹120, how much do 7 kites cost? (a) ₹160 (b) ₹140 (c) ₹121 (d) ₹840
10. 10.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 9 days (d) 10 days
11. 11.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 17 days (d) 6 days
12. 12.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹279 (d) ₹248
13. 13.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 20 days (c) 42 days (d) 8 days
14. 14.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹315 (b) ₹280 (c) ₹175 (d) ₹35
15. 15.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹45 (d) ₹5
16. 16.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹252 (d) ₹288
17. 17.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 13 days (d) 25 days
18. 18.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 7 days (d) 13 days
19. 19.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 7 days (d) 21 days
20. 20.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹117 (b) ₹39 (c) ₹156 (d) ₹195
21. 21.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹150 (d) ₹135
22. 22.If 3 kites cost ₹48, how much do 2 kites cost? (a) ₹47 (b) ₹96 (c) ₹32 (d) ₹48
23. 23.6 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) 5 days (d) 13 days
24. 24.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹161 (b) ₹46 (c) ₹23 (d) ₹184
25. 25.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 9 days
26. 26.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹117 (b) ₹105 (c) ₹104 (d) ₹13
27. 27.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 2 days (d) 1 day
28. 28.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 29 days (d) 1 day
29. 29.If 8 kites cost ₹128, how much do 12 kites cost? (a) ₹208 (b) ₹132 (c) ₹1536 (d) ₹192
30. 30.If 7 kites cost ₹161, how much do 10 kites cost? (a) ₹230 (b) ₹1610 (c) ₹164 (d) ₹253
31. 31.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 14 days
32. 32.If 5 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹14 (b) ₹15 (c) ₹60 (d) ₹12
33. 33.If 7 pens cost ₹77, how much do 3 pens cost? (a) ₹231 (b) ₹33 (c) ₹44 (d) ₹73
34. 34.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 3 days (d) 4 days
35. 35.If 3 pens cost ₹66, how much do 10 pens cost? (a) ₹220 (b) ₹660 (c) ₹73 (d) ₹242
36. 36.If 7 notebooks cost ₹42, how much do 8 notebooks cost? (a) ₹336 (b) ₹43 (c) ₹48 (d) ₹54
37. 37.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹119 (b) ₹102 (c) ₹34 (d) ₹136
38. 38.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹36 (b) ₹162 (c) ₹288 (d) ₹324
39. 39.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 10 days (d) 8 days
40. 40.If 2 notebooks cost ₹34, how much do 3 notebooks cost? (a) ₹35 (b) ₹68 (c) ₹102 (d) ₹51

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