Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 15 · 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.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹149 (d) ₹148
2. 2.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 5 days (c) 21 days (d) 13 days
3. 3.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 12 days
4. 4.If 6 pens cost ₹24, how much do 10 pens cost? (a) ₹240 (b) ₹44 (c) ₹28 (d) ₹40
5. 5.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 4 days
6. 6.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 9 days (d) 15 days
7. 7.If 3 kites cost ₹9, how much do 8 kites cost? (a) ₹27 (b) ₹72 (c) ₹14 (d) ₹24
8. 8.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹155 (d) ₹279
9. 9.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
10. 10.₹506 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹92 (b) ₹253 (c) ₹414 (d) ₹46
11. 11.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 36 days (d) 35 days
12. 12.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹294 (d) ₹196
13. 13.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 8 days (d) 9 days
14. 14.If 5 pens cost ₹40, how much do 9 pens cost? (a) ₹72 (b) ₹80 (c) ₹360 (d) ₹44
15. 15.If 4 notebooks cost ₹84, how much do 8 notebooks cost? (a) ₹168 (b) ₹672 (c) ₹88 (d) ₹189
16. 16.₹342 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹171 (b) ₹304 (c) ₹38 (d) ₹342
17. 17.If 3 notebooks cost ₹39, how much do 4 notebooks cost? (a) ₹65 (b) ₹40 (c) ₹156 (d) ₹52
18. 18.₹330 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹297 (d) ₹330
19. 19.If 2 mangoes cost ₹8, how much do 9 mangoes cost? (a) ₹40 (b) ₹15 (c) ₹72 (d) ₹36
20. 20.If 2 kites cost ₹24, how much do 12 kites cost? (a) ₹288 (b) ₹144 (c) ₹156 (d) ₹34
21. 21.If 6 notebooks cost ₹78, how much do 8 notebooks cost? (a) ₹80 (b) ₹117 (c) ₹624 (d) ₹104
22. 22.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 6 days (d) 7 days
23. 23.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹126 (d) ₹147
24. 24.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 9 days (d) 11 days
25. 25.If 9 pens cost ₹90, how much do 10 pens cost? (a) ₹91 (b) ₹110 (c) ₹100 (d) ₹900
26. 26.If 4 mangoes cost ₹12, how much do 12 mangoes cost? (a) ₹144 (b) ₹36 (c) ₹39 (d) ₹20
27. 27.If 3 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹80 (b) ₹240 (c) ₹31 (d) ₹88
28. 28.If 9 kites cost ₹36, how much do 11 kites cost? (a) ₹48 (b) ₹44 (c) ₹396 (d) ₹38
29. 29.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 52 days (d) 53 days
30. 30.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹30 (c) ₹50 (d) ₹10
31. 31.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹296 (d) ₹259
32. 32.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹14 (c) ₹70 (d) ₹98
33. 33.If 5 notebooks cost ₹85, how much do 6 notebooks cost? (a) ₹510 (b) ₹102 (c) ₹119 (d) ₹86
34. 34.If 3 kites cost ₹63, how much do 7 kites cost? (a) ₹147 (b) ₹168 (c) ₹67 (d) ₹441
35. 35.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹85 (d) ₹119
36. 36.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹104 (b) ₹16 (c) ₹144 (d) ₹64
37. 37.If 4 notebooks cost ₹80, how much do 7 notebooks cost? (a) ₹83 (b) ₹560 (c) ₹160 (d) ₹140
38. 38.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹135 (d) ₹150
39. 39.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹62 (b) ₹93 (c) ₹31 (d) ₹124
40. 40.If 6 notebooks cost ₹96, how much do 8 notebooks cost? (a) ₹98 (b) ₹768 (c) ₹144 (d) ₹128

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