Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 28 · 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. 1.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 11 days (d) 15 days
2. 2.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 3 days (c) 17 days (d) 46 days
3. 3.If 7 kites cost ₹49, how much do 6 kites cost? (a) ₹294 (b) ₹42 (c) ₹48 (d) ₹49
4. 4.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 6 days
5. 5.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 1 day (d) 9 days
6. 6.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹46 (d) ₹230
7. 7.If 8 mangoes cost ₹56, how much do 6 mangoes cost? (a) ₹336 (b) ₹54 (c) ₹42 (d) ₹49
8. 8.If 8 pens cost ₹200, how much do 11 pens cost? (a) ₹300 (b) ₹275 (c) ₹2200 (d) ₹203
9. 9.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹185 (d) ₹222
10. 10.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 27 days (d) 1 day
11. 11.If 3 mangoes cost ₹48, how much do 8 mangoes cost? (a) ₹144 (b) ₹53 (c) ₹128 (d) ₹384
12. 12.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 5 days (d) 6 days
13. 13.If 5 kites cost ₹80, how much do 11 kites cost? (a) ₹86 (b) ₹880 (c) ₹176 (d) ₹192
14. 14.If 7 notebooks cost ₹35, how much do 8 notebooks cost? (a) ₹36 (b) ₹40 (c) ₹280 (d) ₹45
15. 15.If 8 pens cost ₹152, how much do 12 pens cost? (a) ₹1824 (b) ₹228 (c) ₹247 (d) ₹156
16. 16.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹126 (d) ₹91
17. 17.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹80 (b) ₹88 (c) ₹16 (d) ₹96
18. 18.If 7 notebooks cost ₹49, how much do 2 notebooks cost? (a) ₹14 (b) ₹98 (c) ₹21 (d) ₹44
19. 19.If 6 pens cost ₹48, how much do 3 pens cost? (a) ₹45 (b) ₹32 (c) ₹144 (d) ₹24
20. 20.If 9 notebooks cost ₹153, how much do 5 notebooks cost? (a) ₹765 (b) ₹149 (c) ₹85 (d) ₹102
21. 21.If 5 pens cost ₹25, how much do 11 pens cost? (a) ₹31 (b) ₹55 (c) ₹275 (d) ₹60
22. 22.₹190 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹190 (b) ₹95 (c) ₹38 (d) ₹152
23. 23.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹150 (c) ₹30 (d) ₹75
24. 24.If 6 pens cost ₹84, how much do 4 pens cost? (a) ₹336 (b) ₹70 (c) ₹56 (d) ₹82
25. 25.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹50 (d) ₹40
26. 26.If 9 notebooks cost ₹99, how much do 10 notebooks cost? (a) ₹110 (b) ₹100 (c) ₹990 (d) ₹121
27. 27.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹49 (b) ₹343 (c) ₹245 (d) ₹294
28. 28.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹132 (d) ₹198
29. 29.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹79 (c) ₹13 (d) ₹78
30. 30.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹315 (c) ₹225 (d) ₹135
31. 31.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 9 days (d) 15 days
32. 32.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
33. 33.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 26 days (c) 28 days (d) 27 days
34. 34.If 4 mangoes cost ₹80, how much do 5 mangoes cost? (a) ₹400 (b) ₹120 (c) ₹81 (d) ₹100
35. 35.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹51 (d) ₹34
36. 36.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹280 (c) ₹315 (d) ₹175
37. 37.If 9 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹103 (b) ₹60 (c) ₹48 (d) ₹432
38. 38.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹72 (b) ₹60 (c) ₹12 (d) ₹84
39. 39.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 26 days (c) 27 days (d) 9 days
40. 40.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹240 (b) ₹61 (c) ₹80 (d) ₹100

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