Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 440 · 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.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹186 (b) ₹155 (c) ₹217 (d) ₹31
2. 2.If 4 notebooks cost ₹100, how much do 2 notebooks cost? (a) ₹50 (b) ₹200 (c) ₹98 (d) ₹75
3. 3.7 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
4. 4.5 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) 25 days (d) 13 days
5. 5.If 4 notebooks cost ₹28, how much do 11 notebooks cost? (a) ₹84 (b) ₹77 (c) ₹308 (d) ₹35
6. 6.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹116 (d) ₹117
7. 7.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹63 (d) ₹9
8. 8.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 4 days
9. 9.If 6 mangoes cost ₹90, how much do 7 mangoes cost? (a) ₹91 (b) ₹120 (c) ₹630 (d) ₹105
10. 10.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹188 (b) ₹423 (c) ₹470 (d) ₹47
11. 11.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
12. 12.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 12 days (d) 2 days
13. 13.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹42 (c) ₹56 (d) ₹14
14. 14.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 3 days (d) 15 days
15. 15.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 12 days (d) 8 days
16. 16.If 2 pens cost ₹42, how much do 6 pens cost? (a) ₹252 (b) ₹46 (c) ₹147 (d) ₹126
17. 17.If 3 pens cost ₹36, how much do 9 pens cost? (a) ₹120 (b) ₹108 (c) ₹42 (d) ₹324
18. 18.If 5 pens cost ₹50, how much do 7 pens cost? (a) ₹80 (b) ₹52 (c) ₹70 (d) ₹350
19. 19.If 8 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹45 (b) ₹240 (c) ₹36 (d) ₹30
20. 20.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹32 (b) ₹192 (c) ₹96 (d) ₹160
21. 21.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹129 (b) ₹43 (c) ₹215 (d) ₹172
22. 22.If 7 notebooks cost ₹49, how much do 5 notebooks cost? (a) ₹35 (b) ₹42 (c) ₹47 (d) ₹245
23. 23.If 5 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹45 (b) ₹180 (c) ₹44 (d) ₹36
24. 24.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 14 days (d) 8 days
25. 25.If 4 mangoes cost ₹88, how much do 6 mangoes cost? (a) ₹132 (b) ₹154 (c) ₹90 (d) ₹528
26. 26.If 8 kites cost ₹192, how much do 4 kites cost? (a) ₹768 (b) ₹188 (c) ₹120 (d) ₹96
27. 27.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
28. 28.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 9 days (d) 15 days
29. 29.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹144 (c) ₹180 (d) ₹36
30. 30.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹195 (b) ₹120 (c) ₹30 (d) ₹270
31. 31.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 6 days (d) 8 days
32. 32.If 9 notebooks cost ₹180, how much do 12 notebooks cost? (a) ₹240 (b) ₹2160 (c) ₹183 (d) ₹260
33. 33.If 6 kites cost ₹36, how much do 5 kites cost? (a) ₹35 (b) ₹36 (c) ₹30 (d) ₹180
34. 34.If 2 pens cost ₹30, how much do 9 pens cost? (a) ₹270 (b) ₹135 (c) ₹37 (d) ₹150
35. 35.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹152 (b) ₹209 (c) ₹38 (d) ₹266
36. 36.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹333 (d) ₹296
37. 37.If 9 mangoes cost ₹162, how much do 12 mangoes cost? (a) ₹1944 (b) ₹234 (c) ₹165 (d) ₹216
38. 38.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 10 days (c) 16 days (d) 27 days
39. 39.If 9 mangoes cost ₹162, how much do 8 mangoes cost? (a) ₹144 (b) ₹161 (c) ₹1296 (d) ₹162
40. 40.If 3 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹432 (b) ₹160 (c) ₹144 (d) ₹54

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