Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 3 · 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.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹126 (d) ₹18
2. 2.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹52 (b) ₹130 (c) ₹117 (d) ₹13
3. 3.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 20 days
4. 4.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹171 (b) ₹190 (c) ₹19 (d) ₹95
5. 5.If 6 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹270 (b) ₹45 (c) ₹33 (d) ₹50
6. 6.If 5 kites cost ₹125, how much do 4 kites cost? (a) ₹125 (b) ₹100 (c) ₹124 (d) ₹500
7. 7.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹48 (b) ₹25 (c) ₹36 (d) ₹72
8. 8.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹110 (d) ₹88
9. 9.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 15 days (c) 37 days (d) 36 days
10. 10.If 5 mangoes cost ₹30, how much do 10 mangoes cost? (a) ₹35 (b) ₹60 (c) ₹66 (d) ₹300
11. 11.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹42 (b) ₹294 (c) ₹231 (d) ₹168
12. 12.If 3 notebooks cost ₹60, how much do 12 notebooks cost? (a) ₹720 (b) ₹240 (c) ₹260 (d) ₹69
13. 13.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹215 (b) ₹258 (c) ₹172 (d) ₹43
14. 14.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 13 days (d) 12 days
15. 15.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 11 days (c) 19 days (d) 30 days
16. 16.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹430 (d) ₹387
17. 17.If 5 pens cost ₹35, how much do 3 pens cost? (a) ₹28 (b) ₹21 (c) ₹105 (d) ₹33
18. 18.If 4 mangoes cost ₹72, how much do 12 mangoes cost? (a) ₹864 (b) ₹234 (c) ₹80 (d) ₹216
19. 19.If 3 mangoes cost ₹33, how much do 4 mangoes cost? (a) ₹44 (b) ₹132 (c) ₹55 (d) ₹34
20. 20.₹294 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹147 (b) ₹42 (c) ₹210 (d) ₹84
21. 21.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹119 (d) ₹102
22. 22.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 14 days (d) 15 days
23. 23.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹80 (c) ₹16 (d) ₹72
24. 24.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹84 (c) ₹63 (d) ₹105
25. 25.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹147 (c) ₹126 (d) ₹105
26. 26.If 8 notebooks cost ₹160, how much do 11 notebooks cost? (a) ₹1760 (b) ₹240 (c) ₹220 (d) ₹163
27. 27.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹55 (b) ₹70 (c) ₹40 (d) ₹10
28. 28.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 10 days (d) 3 days
29. 29.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 17 days (c) 43 days (d) 7 days
30. 30.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 9 days (d) 14 days
31. 31.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 2 days (d) 10 days
32. 32.If 5 kites cost ₹65, how much do 10 kites cost? (a) ₹650 (b) ₹143 (c) ₹70 (d) ₹130
33. 33.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 8 days (d) 14 days
34. 34.If 3 pens cost ₹18, how much do 10 pens cost? (a) ₹60 (b) ₹66 (c) ₹180 (d) ₹25
35. 35.If 6 mangoes cost ₹66, how much do 9 mangoes cost? (a) ₹69 (b) ₹594 (c) ₹110 (d) ₹99
36. 36.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹45 (b) ₹25 (c) ₹5 (d) ₹50
37. 37.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 17 days (c) 4 days (d) 16 days
38. 38.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 6 days (d) 4 days
39. 39.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 22 days (d) 23 days
40. 40.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 11 days

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