Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 931 · 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.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹52 (b) ₹104 (c) ₹78 (d) ₹26
2. 2.If 8 notebooks cost ₹160, how much do 9 notebooks cost? (a) ₹161 (b) ₹1440 (c) ₹200 (d) ₹180
3. 3.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
4. 4.If 4 mangoes cost ₹64, how much do 7 mangoes cost? (a) ₹112 (b) ₹448 (c) ₹128 (d) ₹67
5. 5.If 6 mangoes cost ₹150, how much do 10 mangoes cost? (a) ₹154 (b) ₹250 (c) ₹1500 (d) ₹275
6. 6.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹48 (b) ₹288 (c) ₹264 (d) ₹240
7. 7.₹275 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹75 (b) ₹225 (c) ₹25 (d) ₹200
8. 8.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹54 (b) ₹119 (c) ₹102 (d) ₹306
9. 9.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 32 days (c) 2 days (d) 33 days
10. 10.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 19 days (d) 18 days
11. 11.If 6 kites cost ₹90, how much do 12 kites cost? (a) ₹195 (b) ₹180 (c) ₹1080 (d) ₹96
12. 12.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹234 (b) ₹52 (c) ₹26 (d) ₹143
13. 13.If 2 kites cost ₹14, how much do 11 kites cost? (a) ₹23 (b) ₹84 (c) ₹154 (d) ₹77
14. 14.If 4 notebooks cost ₹84, how much do 11 notebooks cost? (a) ₹91 (b) ₹252 (c) ₹924 (d) ₹231
15. 15.3 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
16. 16.If 2 mangoes cost ₹30, how much do 9 mangoes cost? (a) ₹135 (b) ₹37 (c) ₹150 (d) ₹270
17. 17.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 26 days (c) 17 days (d) 27 days
18. 18.If 9 mangoes cost ₹198, how much do 7 mangoes cost? (a) ₹154 (b) ₹176 (c) ₹1386 (d) ₹196
19. 19.If 2 notebooks cost ₹26, how much do 5 notebooks cost? (a) ₹130 (b) ₹65 (c) ₹78 (d) ₹29
20. 20.₹180 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹90 (d) ₹180
21. 21.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹36 (b) ₹324 (c) ₹180 (d) ₹252
22. 22.If 9 kites cost ₹153, how much do 4 kites cost? (a) ₹148 (b) ₹612 (c) ₹68 (d) ₹85
23. 23.If 5 mangoes cost ₹65, how much do 11 mangoes cost? (a) ₹143 (b) ₹156 (c) ₹715 (d) ₹71
24. 24.If 3 notebooks cost ₹51, how much do 6 notebooks cost? (a) ₹306 (b) ₹119 (c) ₹54 (d) ₹102
25. 25.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹29 (b) ₹35 (c) ₹28 (d) ₹7
26. 26.If 9 kites cost ₹27, how much do 6 kites cost? (a) ₹21 (b) ₹18 (c) ₹24 (d) ₹162
27. 27.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹17 (b) ₹103 (c) ₹119 (d) ₹102
28. 28.If 5 notebooks cost ₹100, how much do 3 notebooks cost? (a) ₹60 (b) ₹80 (c) ₹98 (d) ₹300
29. 29.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 10 days (d) 13 days
30. 30.If 8 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹432 (b) ₹72 (c) ₹54 (d) ₹139
31. 31.If 5 kites cost ₹125, how much do 4 kites cost? (a) ₹124 (b) ₹125 (c) ₹100 (d) ₹500
32. 32.If 5 mangoes cost ₹60, how much do 8 mangoes cost? (a) ₹108 (b) ₹96 (c) ₹480 (d) ₹63
33. 33.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 11 days (d) 16 days
34. 34.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹162 (b) ₹18 (c) ₹99 (d) ₹36
35. 35.If 9 mangoes cost ₹27, how much do 3 mangoes cost? (a) ₹81 (b) ₹9 (c) ₹21 (d) ₹12
36. 36.If 2 kites cost ₹8, how much do 12 kites cost? (a) ₹18 (b) ₹96 (c) ₹52 (d) ₹48
37. 37.If 4 notebooks cost ₹60, how much do 12 notebooks cost? (a) ₹195 (b) ₹180 (c) ₹68 (d) ₹720
38. 38.If 6 pens cost ₹96, how much do 2 pens cost? (a) ₹92 (b) ₹192 (c) ₹32 (d) ₹48
39. 39.If 7 notebooks cost ₹28, how much do 9 notebooks cost? (a) ₹30 (b) ₹252 (c) ₹40 (d) ₹36
40. 40.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹196 (b) ₹98 (c) ₹147 (d) ₹49

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