Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 448 · 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.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹71 (d) ₹105
2. 2.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 22 days (c) 15 days (d) 23 days
3. 3.₹240 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹24 (b) ₹120 (c) ₹168 (d) ₹72
4. 4.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹39 (c) ₹19 (d) ₹38
5. 5.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 10 days (d) 4 days
6. 6.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹63 (b) ₹105 (c) ₹126 (d) ₹21
7. 7.If 7 pens cost ₹175, how much do 4 pens cost? (a) ₹700 (b) ₹100 (c) ₹125 (d) ₹172
8. 8.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹17 (b) ₹136 (c) ₹153 (d) ₹85
9. 9.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹100 (c) ₹50 (d) ₹250
10. 10.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 32 days (c) 33 days (d) 17 days
11. 11.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹45 (b) ₹9 (c) ₹63 (d) ₹54
12. 12.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹62 (b) ₹31 (c) ₹248 (d) ₹217
13. 13.If 5 pens cost ₹20, how much do 6 pens cost? (a) ₹120 (b) ₹24 (c) ₹28 (d) ₹21
14. 14.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 10 days
15. 15.If 2 pens cost ₹26, how much do 3 pens cost? (a) ₹78 (b) ₹52 (c) ₹39 (d) ₹27
16. 16.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹224 (d) ₹96
17. 17.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 14 days (d) 5 days
18. 18.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹242 (b) ₹176 (c) ₹44 (d) ₹308
19. 19.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹105 (b) ₹189 (c) ₹168 (d) ₹21
20. 20.If 5 pens cost ₹30, how much do 2 pens cost? (a) ₹12 (b) ₹27 (c) ₹60 (d) ₹18
21. 21.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 15 days (d) 8 days
22. 22.If 7 pens cost ₹175, how much do 5 pens cost? (a) ₹125 (b) ₹150 (c) ₹875 (d) ₹173
23. 23.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹187 (b) ₹136 (c) ₹238 (d) ₹34
24. 24.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹56 (b) ₹98 (c) ₹140 (d) ₹28
25. 25.5 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
26. 26.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 25 days (c) 4 days (d) 5 days
27. 27.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹45 (c) ₹40 (d) ₹5
28. 28.If 6 mangoes cost ₹48, how much do 3 mangoes cost? (a) ₹45 (b) ₹144 (c) ₹24 (d) ₹32
29. 29.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 16 days (d) 1 day
30. 30.If 2 mangoes cost ₹36, how much do 6 mangoes cost? (a) ₹126 (b) ₹40 (c) ₹216 (d) ₹108
31. 31.₹162 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹36 (b) ₹126 (c) ₹81 (d) ₹18
32. 32.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 13 days (d) 8 days
33. 33.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 18 days (d) 8 days
34. 34.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 7 days (c) 19 days (d) 53 days
35. 35.₹270 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹135 (d) ₹225
36. 36.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹35 (b) ₹40 (c) ₹20 (d) ₹5
37. 37.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹294 (b) ₹49 (c) ₹343 (d) ₹245
38. 38.If 4 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹105 (b) ₹85 (c) ₹420 (d) ₹126
39. 39.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹39 (b) ₹273 (c) ₹234 (d) ₹195
40. 40.If 9 pens cost ₹198, how much do 7 pens cost? (a) ₹196 (b) ₹154 (c) ₹1386 (d) ₹176

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