Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 567 · 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. 1.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 1 day (d) 21 days
2. 2.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹165 (b) ₹33 (c) ₹132 (d) ₹99
3. 3.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹65 (c) ₹13 (d) ₹104
4. 4.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹45 (b) ₹27 (c) ₹9 (d) ₹36
5. 5.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 54 days (b) 55 days (c) 5 days (d) 19 days
6. 6.If 4 mangoes cost ₹44, how much do 3 mangoes cost? (a) ₹43 (b) ₹44 (c) ₹33 (d) ₹132
7. 7.If 8 mangoes cost ₹104, how much do 9 mangoes cost? (a) ₹117 (b) ₹130 (c) ₹105 (d) ₹936
8. 8.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 9 days (d) 13 days
9. 9.If 8 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹35 (b) ₹120 (c) ₹15 (d) ₹20
10. 10.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹30 (c) ₹24 (d) ₹36
11. 11.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 12 days (d) 15 days
12. 12.If 6 pens cost ₹30, how much do 7 pens cost? (a) ₹40 (b) ₹210 (c) ₹31 (d) ₹35
13. 13.If 2 kites cost ₹10, how much do 5 kites cost? (a) ₹25 (b) ₹30 (c) ₹50 (d) ₹13
14. 14.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹294 (b) ₹42 (c) ₹126 (d) ₹210
15. 15.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 2 days (d) 11 days
16. 16.If 8 kites cost ₹48, how much do 5 kites cost? (a) ₹45 (b) ₹240 (c) ₹30 (d) ₹36
17. 17.₹240 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹120 (b) ₹240 (c) ₹40 (d) ₹200
18. 18.If 7 kites cost ₹119, how much do 11 kites cost? (a) ₹123 (b) ₹1309 (c) ₹187 (d) ₹204
19. 19.If 6 notebooks cost ₹48, how much do 7 notebooks cost? (a) ₹336 (b) ₹49 (c) ₹64 (d) ₹56
20. 20.If 4 notebooks cost ₹88, how much do 5 notebooks cost? (a) ₹132 (b) ₹89 (c) ₹440 (d) ₹110
21. 21.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹140 (b) ₹315 (c) ₹350 (d) ₹35
22. 22.If 4 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹70 (b) ₹54 (c) ₹36 (d) ₹144
23. 23.₹130 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹65 (d) ₹130
24. 24.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 12 days (d) 11 days
25. 25.If 2 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹144 (b) ₹38 (c) ₹90 (d) ₹72
26. 26.If 8 notebooks cost ₹32, how much do 9 notebooks cost? (a) ₹40 (b) ₹288 (c) ₹36 (d) ₹33
27. 27.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹21 (c) ₹7 (d) ₹14
28. 28.If 4 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹120 (b) ₹25 (c) ₹36 (d) ₹30
29. 29.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 5 days (d) 4 days
30. 30.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹40 (d) ₹35
31. 31.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 21 days (c) 20 days (d) 13 days
32. 32.If 4 pens cost ₹24, how much do 12 pens cost? (a) ₹78 (b) ₹72 (c) ₹32 (d) ₹288
33. 33.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹87 (b) ₹116 (c) ₹145 (d) ₹29
34. 34.If 2 pens cost ₹22, how much do 9 pens cost? (a) ₹99 (b) ₹29 (c) ₹198 (d) ₹110
35. 35.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹51 (c) ₹34 (d) ₹68
36. 36.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹273 (b) ₹336 (c) ₹210 (d) ₹42
37. 37.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹51 (d) ₹102
38. 38.If 2 mangoes cost ₹48, how much do 6 mangoes cost? (a) ₹52 (b) ₹288 (c) ₹168 (d) ₹144
39. 39.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹280 (b) ₹35 (c) ₹245 (d) ₹140
40. 40.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 23 days (c) 12 days (d) 24 days

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