Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 443 · 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.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹195 (b) ₹351 (c) ₹390 (d) ₹39
2. 2.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 4 days (d) 5 days
3. 3.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹108 (b) ₹66 (c) ₹12 (d) ₹24
4. 4.If 9 mangoes cost ₹144, how much do 12 mangoes cost? (a) ₹208 (b) ₹147 (c) ₹1728 (d) ₹192
5. 5.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 14 days (d) 16 days
6. 6.If 6 kites cost ₹150, how much do 7 kites cost? (a) ₹175 (b) ₹151 (c) ₹200 (d) ₹1050
7. 7.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹172 (b) ₹43 (c) ₹301 (d) ₹344
8. 8.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹42 (b) ₹294 (c) ₹336 (d) ₹168
9. 9.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 2 days (d) 14 days
10. 10.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 7 days (d) 28 days
11. 11.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹81 (b) ₹72 (c) ₹18 (d) ₹90
12. 12.If 4 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹45 (b) ₹90 (c) ₹100 (d) ₹360
13. 13.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹32 (b) ₹72 (c) ₹16 (d) ₹112
14. 14.If 2 pens cost ₹32, how much do 3 pens cost? (a) ₹48 (b) ₹64 (c) ₹33 (d) ₹96
15. 15.If 7 pens cost ₹161, how much do 6 pens cost? (a) ₹966 (b) ₹161 (c) ₹160 (d) ₹138
16. 16.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹46 (b) ₹276 (c) ₹138 (d) ₹230
17. 17.If 7 mangoes cost ₹161, how much do 8 mangoes cost? (a) ₹1288 (b) ₹207 (c) ₹162 (d) ₹184
18. 18.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹24 (b) ₹8 (c) ₹64 (d) ₹44
19. 19.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹70 (b) ₹10 (c) ₹80 (d) ₹40
20. 20.If 2 notebooks cost ₹38, how much do 10 notebooks cost? (a) ₹190 (b) ₹46 (c) ₹209 (d) ₹380
21. 21.If 9 notebooks cost ₹117, how much do 11 notebooks cost? (a) ₹143 (b) ₹1287 (c) ₹156 (d) ₹119
22. 22.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹46 (b) ₹276 (c) ₹230 (d) ₹253
23. 23.If 8 pens cost ₹136, how much do 9 pens cost? (a) ₹137 (b) ₹153 (c) ₹1224 (d) ₹170
24. 24.If 8 kites cost ₹48, how much do 12 kites cost? (a) ₹72 (b) ₹52 (c) ₹576 (d) ₹78
25. 25.If 9 pens cost ₹207, how much do 2 pens cost? (a) ₹46 (b) ₹414 (c) ₹69 (d) ₹200
26. 26.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹378 (b) ₹189 (c) ₹42 (d) ₹336
27. 27.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹8 (b) ₹20 (c) ₹40 (d) ₹32
28. 28.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 11 days (d) 1 day
29. 29.If 4 kites cost ₹80, how much do 10 kites cost? (a) ₹86 (b) ₹220 (c) ₹800 (d) ₹200
30. 30.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹270 (b) ₹27 (c) ₹108 (d) ₹243
31. 31.If 3 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹22 (b) ₹84 (c) ₹35 (d) ₹28
32. 32.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 1 day
33. 33.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹42 (b) ₹336 (c) ₹273 (d) ₹210
34. 34.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹45 (d) ₹27
35. 35.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹44 (d) ₹33
36. 36.If 6 pens cost ₹78, how much do 5 pens cost? (a) ₹77 (b) ₹65 (c) ₹390 (d) ₹78
37. 37.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹60 (b) ₹15 (c) ₹30 (d) ₹45
38. 38.If 5 kites cost ₹90, how much do 7 kites cost? (a) ₹630 (b) ₹126 (c) ₹144 (d) ₹92
39. 39.If 2 notebooks cost ₹34, how much do 4 notebooks cost? (a) ₹85 (b) ₹36 (c) ₹136 (d) ₹68
40. 40.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹162 (b) ₹189 (c) ₹27 (d) ₹163

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