Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 131 · 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.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹54 (d) ₹48
2. 2.If 5 notebooks cost ₹25, how much do 2 notebooks cost? (a) ₹50 (b) ₹10 (c) ₹15 (d) ₹22
3. 3.If 8 pens cost ₹80, how much do 6 pens cost? (a) ₹78 (b) ₹60 (c) ₹70 (d) ₹480
4. 4.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹45 (b) ₹11 (c) ₹44 (d) ₹55
5. 5.If 7 mangoes cost ₹49, how much do 3 mangoes cost? (a) ₹28 (b) ₹147 (c) ₹21 (d) ₹45
6. 6.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹210 (d) ₹140
7. 7.If 8 mangoes cost ₹200, how much do 9 mangoes cost? (a) ₹250 (b) ₹1800 (c) ₹201 (d) ₹225
8. 8.If 8 pens cost ₹24, how much do 4 pens cost? (a) ₹20 (b) ₹96 (c) ₹15 (d) ₹12
9. 9.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 9 days (d) 24 days
10. 10.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 17 days (d) 7 days
11. 11.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 46 days (b) 3 days (c) 45 days (d) 17 days
12. 12.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 17 days (d) 11 days
13. 13.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 17 days (d) 12 days
14. 14.4 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) 18 days (d) 7 days
15. 15.If 6 kites cost ₹90, how much do 7 kites cost? (a) ₹630 (b) ₹91 (c) ₹120 (d) ₹105
16. 16.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 55 days (c) 54 days (d) 19 days
17. 17.If 3 kites cost ₹63, how much do 6 kites cost? (a) ₹126 (b) ₹66 (c) ₹147 (d) ₹378
18. 18.If 2 notebooks cost ₹6, how much do 5 notebooks cost? (a) ₹9 (b) ₹30 (c) ₹15 (d) ₹18
19. 19.₹287 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹246 (b) ₹247 (c) ₹41 (d) ₹287
20. 20.If 7 kites cost ₹91, how much do 2 kites cost? (a) ₹26 (b) ₹182 (c) ₹39 (d) ₹86
21. 21.If 8 notebooks cost ₹112, how much do 4 notebooks cost? (a) ₹56 (b) ₹448 (c) ₹70 (d) ₹108
22. 22.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 6 days (d) 4 days
23. 23.If 3 kites cost ₹15, how much do 9 kites cost? (a) ₹21 (b) ₹50 (c) ₹45 (d) ₹135
24. 24.If 6 pens cost ₹66, how much do 12 pens cost? (a) ₹143 (b) ₹132 (c) ₹792 (d) ₹72
25. 25.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 30 days (c) 11 days (d) 31 days
26. 26.If 8 pens cost ₹120, how much do 2 pens cost? (a) ₹114 (b) ₹45 (c) ₹240 (d) ₹30
27. 27.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹144 (b) ₹240 (c) ₹48 (d) ₹192
28. 28.If 5 mangoes cost ₹50, how much do 9 mangoes cost? (a) ₹450 (b) ₹90 (c) ₹54 (d) ₹100
29. 29.If 6 kites cost ₹78, how much do 5 kites cost? (a) ₹65 (b) ₹390 (c) ₹77 (d) ₹78
30. 30.If 4 mangoes cost ₹88, how much do 6 mangoes cost? (a) ₹154 (b) ₹528 (c) ₹132 (d) ₹90
31. 31.If 2 notebooks cost ₹8, how much do 12 notebooks cost? (a) ₹96 (b) ₹18 (c) ₹48 (d) ₹52
32. 32.If 3 notebooks cost ₹39, how much do 8 notebooks cost? (a) ₹104 (b) ₹117 (c) ₹312 (d) ₹44
33. 33.If 4 mangoes cost ₹56, how much do 8 mangoes cost? (a) ₹448 (b) ₹112 (c) ₹60 (d) ₹126
34. 34.If 2 pens cost ₹46, how much do 5 pens cost? (a) ₹49 (b) ₹115 (c) ₹138 (d) ₹230
35. 35.If 5 notebooks cost ₹80, how much do 2 notebooks cost? (a) ₹160 (b) ₹48 (c) ₹77 (d) ₹32
36. 36.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
37. 37.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 19 days (c) 16 days (d) 18 days
38. 38.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹185 (b) ₹111 (c) ₹37 (d) ₹148
39. 39.If 2 kites cost ₹34, how much do 5 kites cost? (a) ₹102 (b) ₹37 (c) ₹170 (d) ₹85
40. 40.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹30 (c) ₹6 (d) ₹18

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