Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 464 · 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.₹319 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹58 (b) ₹261 (c) ₹290 (d) ₹29
2. 2.If 5 notebooks cost ₹120, how much do 11 notebooks cost? (a) ₹288 (b) ₹1320 (c) ₹126 (d) ₹264
3. 3.If 3 pens cost ₹69, how much do 12 pens cost? (a) ₹276 (b) ₹299 (c) ₹78 (d) ₹828
4. 4.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹38 (b) ₹304 (c) ₹209 (d) ₹114
5. 5.₹352 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹176 (b) ₹64 (c) ₹32 (d) ₹288
6. 6.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹75 (b) ₹111 (c) ₹37 (d) ₹74
7. 7.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹111 (b) ₹185 (c) ₹37 (d) ₹259
8. 8.₹133 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹95 (d) ₹57
9. 9.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹46 (b) ₹23 (c) ₹230 (d) ₹207
10. 10.If 9 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹28 (b) ₹33 (c) ₹30 (d) ₹270
11. 11.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹175 (d) ₹150
12. 12.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹21 (d) ₹12
13. 13.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹11 (b) ₹55 (c) ₹77 (d) ₹66
14. 14.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹168 (b) ₹210 (c) ₹42 (d) ₹189
15. 15.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 14 days (d) 15 days
16. 16.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹180 (b) ₹90 (c) ₹160 (d) ₹20
17. 17.If 9 notebooks cost ₹54, how much do 11 notebooks cost? (a) ₹72 (b) ₹594 (c) ₹56 (d) ₹66
18. 18.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 21 days (d) 13 days
19. 19.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹192 (b) ₹48 (c) ₹240 (d) ₹120
20. 20.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 35 days (d) 36 days
21. 21.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹144 (c) ₹36 (d) ₹126
22. 22.If 9 kites cost ₹171, how much do 7 kites cost? (a) ₹1197 (b) ₹169 (c) ₹152 (d) ₹133
23. 23.If 5 mangoes cost ₹95, how much do 6 mangoes cost? (a) ₹114 (b) ₹96 (c) ₹133 (d) ₹570
24. 24.If 2 kites cost ₹8, how much do 5 kites cost? (a) ₹20 (b) ₹24 (c) ₹11 (d) ₹40
25. 25.If 8 mangoes cost ₹176, how much do 9 mangoes cost? (a) ₹198 (b) ₹177 (c) ₹1584 (d) ₹220
26. 26.If 5 pens cost ₹90, how much do 3 pens cost? (a) ₹88 (b) ₹270 (c) ₹72 (d) ₹54
27. 27.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹62 (b) ₹93 (c) ₹124 (d) ₹31
28. 28.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 11 days (d) 10 days
29. 29.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹63 (b) ₹18 (c) ₹126 (d) ₹108
30. 30.If 9 kites cost ₹126, how much do 10 kites cost? (a) ₹1260 (b) ₹154 (c) ₹127 (d) ₹140
31. 31.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 17 days (d) 16 days
32. 32.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹14 (d) ₹70
33. 33.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹336 (b) ₹231 (c) ₹42 (d) ₹126
34. 34.If 5 pens cost ₹90, how much do 8 pens cost? (a) ₹144 (b) ₹93 (c) ₹162 (d) ₹720
35. 35.If 2 pens cost ₹28, how much do 9 pens cost? (a) ₹126 (b) ₹35 (c) ₹252 (d) ₹140
36. 36.If 4 mangoes cost ₹16, how much do 10 mangoes cost? (a) ₹160 (b) ₹44 (c) ₹40 (d) ₹22
37. 37.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 11 days (d) 6 days
38. 38.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 4 days
39. 39.₹451 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹287 (b) ₹41 (c) ₹328 (d) ₹164
40. 40.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 36 days (d) 6 days

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