Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 123 · 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.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹132 (d) ₹110
2. 2.If 9 kites cost ₹180, how much do 11 kites cost? (a) ₹182 (b) ₹220 (c) ₹1980 (d) ₹240
3. 3.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹78 (b) ₹91 (c) ₹26 (d) ₹104
4. 4.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 14 days (d) 7 days
5. 5.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 24 days (d) 8 days
6. 6.If 6 notebooks cost ₹114, how much do 8 notebooks cost? (a) ₹116 (b) ₹152 (c) ₹912 (d) ₹171
7. 7.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹132 (b) ₹22 (c) ₹154 (d) ₹110
8. 8.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
9. 9.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹96 (b) ₹80 (c) ₹112 (d) ₹16
10. 10.₹128 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹64 (d) ₹48
11. 11.If 7 notebooks cost ₹112, how much do 12 notebooks cost? (a) ₹192 (b) ₹117 (c) ₹1344 (d) ₹208
12. 12.₹352 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹288 (b) ₹176 (c) ₹32 (d) ₹64
13. 13.If 3 pens cost ₹60, how much do 5 pens cost? (a) ₹120 (b) ₹62 (c) ₹300 (d) ₹100
14. 14.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 16 days (d) 17 days
15. 15.If 4 notebooks cost ₹60, how much do 9 notebooks cost? (a) ₹65 (b) ₹540 (c) ₹150 (d) ₹135
16. 16.If 9 mangoes cost ₹216, how much do 11 mangoes cost? (a) ₹2376 (b) ₹264 (c) ₹288 (d) ₹218
17. 17.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹145 (d) ₹116
18. 18.If 2 notebooks cost ₹28, how much do 12 notebooks cost? (a) ₹336 (b) ₹168 (c) ₹38 (d) ₹182
19. 19.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹234 (b) ₹39 (c) ₹78 (d) ₹195
20. 20.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 8 days (d) 12 days
21. 21.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹62 (b) ₹124 (c) ₹31 (d) ₹93
22. 22.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹207 (b) ₹115 (c) ₹23 (d) ₹161
23. 23.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹81 (b) ₹135 (c) ₹27 (d) ₹108
24. 24.If 8 kites cost ₹152, how much do 11 kites cost? (a) ₹228 (b) ₹155 (c) ₹1672 (d) ₹209
25. 25.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹119 (b) ₹34 (c) ₹238 (d) ₹204
26. 26.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 14 days (d) 2 days
27. 27.If 4 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹99 (b) ₹108 (c) ₹396 (d) ₹43
28. 28.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹105 (d) ₹147
29. 29.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹20 (b) ₹110 (c) ₹180 (d) ₹40
30. 30.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 14 days (d) 19 days
31. 31.If 9 notebooks cost ₹144, how much do 2 notebooks cost? (a) ₹288 (b) ₹137 (c) ₹48 (d) ₹32
32. 32.If 8 notebooks cost ₹160, how much do 7 notebooks cost? (a) ₹159 (b) ₹160 (c) ₹1120 (d) ₹140
33. 33.If 4 kites cost ₹84, how much do 7 kites cost? (a) ₹588 (b) ₹87 (c) ₹168 (d) ₹147
34. 34.If 6 notebooks cost ₹18, how much do 12 notebooks cost? (a) ₹36 (b) ₹24 (c) ₹216 (d) ₹39
35. 35.If 9 mangoes cost ₹81, how much do 8 mangoes cost? (a) ₹648 (b) ₹80 (c) ₹81 (d) ₹72
36. 36.If 5 pens cost ₹80, how much do 9 pens cost? (a) ₹160 (b) ₹84 (c) ₹720 (d) ₹144
37. 37.If 6 notebooks cost ₹96, how much do 11 notebooks cost? (a) ₹101 (b) ₹1056 (c) ₹176 (d) ₹192
38. 38.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹36 (c) ₹72 (d) ₹108
39. 39.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹108 (b) ₹18 (c) ₹90 (d) ₹126
40. 40.If 7 mangoes cost ₹147, how much do 6 mangoes cost? (a) ₹146 (b) ₹147 (c) ₹882 (d) ₹126

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