Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 599 · 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.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹112 (d) ₹80
2. 2.If 4 mangoes cost ₹60, how much do 2 mangoes cost? (a) ₹45 (b) ₹58 (c) ₹120 (d) ₹30
3. 3.If 2 pens cost ₹6, how much do 4 pens cost? (a) ₹15 (b) ₹8 (c) ₹24 (d) ₹12
4. 4.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
5. 5.If 6 notebooks cost ₹30, how much do 12 notebooks cost? (a) ₹36 (b) ₹60 (c) ₹360 (d) ₹65
6. 6.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 7 days (d) 5 days
7. 7.If 3 pens cost ₹45, how much do 9 pens cost? (a) ₹51 (b) ₹405 (c) ₹150 (d) ₹135
8. 8.If 8 pens cost ₹192, how much do 7 pens cost? (a) ₹192 (b) ₹1344 (c) ₹191 (d) ₹168
9. 9.If 4 pens cost ₹16, how much do 11 pens cost? (a) ₹23 (b) ₹44 (c) ₹48 (d) ₹176
10. 10.If 5 pens cost ₹115, how much do 6 pens cost? (a) ₹690 (b) ₹116 (c) ₹138 (d) ₹161
11. 11.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 12 days
12. 12.If 3 notebooks cost ₹72, how much do 2 notebooks cost? (a) ₹144 (b) ₹71 (c) ₹72 (d) ₹48
13. 13.If 5 kites cost ₹45, how much do 10 kites cost? (a) ₹450 (b) ₹99 (c) ₹50 (d) ₹90
14. 14.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 4 days (d) 3 days
15. 15.If 3 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹72 (b) ₹192 (c) ₹64 (d) ₹29
16. 16.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹165 (b) ₹198 (c) ₹132 (d) ₹33
17. 17.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹17 (b) ₹69 (c) ₹68 (d) ₹85
18. 18.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹81 (b) ₹36 (c) ₹9 (d) ₹90
19. 19.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹77 (d) ₹14
20. 20.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 10 days (c) 7 days (d) 18 days
21. 21.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 25 days (d) 13 days
22. 22.If 5 mangoes cost ₹50, how much do 3 mangoes cost? (a) ₹40 (b) ₹48 (c) ₹150 (d) ₹30
23. 23.If 2 pens cost ₹40, how much do 5 pens cost? (a) ₹100 (b) ₹120 (c) ₹200 (d) ₹43
24. 24.If 3 pens cost ₹69, how much do 9 pens cost? (a) ₹207 (b) ₹621 (c) ₹230 (d) ₹75
25. 25.If 8 notebooks cost ₹88, how much do 4 notebooks cost? (a) ₹84 (b) ₹352 (c) ₹44 (d) ₹55
26. 26.If 6 notebooks cost ₹138, how much do 10 notebooks cost? (a) ₹142 (b) ₹1380 (c) ₹253 (d) ₹230
27. 27.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹287 (b) ₹246 (c) ₹41 (d) ₹205
28. 28.If 4 kites cost ₹64, how much do 10 kites cost? (a) ₹640 (b) ₹160 (c) ₹176 (d) ₹70
29. 29.If 8 notebooks cost ₹152, how much do 3 notebooks cost? (a) ₹76 (b) ₹456 (c) ₹147 (d) ₹57
30. 30.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹124 (b) ₹62 (c) ₹93 (d) ₹31
31. 31.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹196 (b) ₹140 (c) ₹28 (d) ₹252
32. 32.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹77 (b) ₹19 (c) ₹76 (d) ₹95
33. 33.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 11 days
34. 34.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 6 days (d) 5 days
35. 35.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 23 days (c) 15 days (d) 22 days
36. 36.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹21 (d) ₹20
37. 37.If 6 pens cost ₹108, how much do 11 pens cost? (a) ₹113 (b) ₹216 (c) ₹198 (d) ₹1188
38. 38.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹72 (d) ₹48
39. 39.If 3 pens cost ₹63, how much do 6 pens cost? (a) ₹147 (b) ₹66 (c) ₹378 (d) ₹126
40. 40.If 8 kites cost ₹56, how much do 3 kites cost? (a) ₹51 (b) ₹21 (c) ₹28 (d) ₹168

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