Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 235 · 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. 1.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 5 days (d) 14 days
2. 2.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 3 days (d) 12 days
3. 3.If 9 pens cost ₹135, how much do 2 pens cost? (a) ₹45 (b) ₹30 (c) ₹270 (d) ₹128
4. 4.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹294 (b) ₹252 (c) ₹147 (d) ₹42
5. 5.If 9 mangoes cost ₹207, how much do 10 mangoes cost? (a) ₹253 (b) ₹2070 (c) ₹208 (d) ₹230
6. 6.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 1 day (d) 2 days
7. 7.If 3 mangoes cost ₹24, how much do 12 mangoes cost? (a) ₹33 (b) ₹288 (c) ₹104 (d) ₹96
8. 8.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹78 (d) ₹312
9. 9.If 3 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹73 (b) ₹120 (c) ₹288 (d) ₹96
10. 10.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 7 days
11. 11.If 6 pens cost ₹42, how much do 9 pens cost? (a) ₹378 (b) ₹63 (c) ₹70 (d) ₹45
12. 12.If 8 notebooks cost ₹128, how much do 2 notebooks cost? (a) ₹256 (b) ₹48 (c) ₹32 (d) ₹122
13. 13.If 9 mangoes cost ₹198, how much do 7 mangoes cost? (a) ₹1386 (b) ₹196 (c) ₹154 (d) ₹176
14. 14.If 9 notebooks cost ₹90, how much do 5 notebooks cost? (a) ₹50 (b) ₹86 (c) ₹450 (d) ₹60
15. 15.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹378 (d) ₹294
16. 16.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹98 (b) ₹28 (c) ₹56 (d) ₹140
17. 17.If 2 notebooks cost ₹22, how much do 9 notebooks cost? (a) ₹198 (b) ₹99 (c) ₹29 (d) ₹110
18. 18.If 2 notebooks cost ₹38, how much do 8 notebooks cost? (a) ₹44 (b) ₹304 (c) ₹171 (d) ₹152
19. 19.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 15 days (d) 14 days
20. 20.If 3 pens cost ₹72, how much do 5 pens cost? (a) ₹144 (b) ₹120 (c) ₹360 (d) ₹74
21. 21.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 33 days (d) 32 days
22. 22.If 9 notebooks cost ₹153, how much do 7 notebooks cost? (a) ₹1071 (b) ₹151 (c) ₹119 (d) ₹136
23. 23.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹222 (d) ₹185
24. 24.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 11 days (d) 15 days
25. 25.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹105 (c) ₹35 (d) ₹140
26. 26.If 4 mangoes cost ₹28, how much do 7 mangoes cost? (a) ₹56 (b) ₹49 (c) ₹196 (d) ₹31
27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 2 days (d) 4 days
28. 28.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 21 days (d) 6 days
29. 29.5 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
30. 30.If 3 mangoes cost ₹63, how much do 5 mangoes cost? (a) ₹65 (b) ₹126 (c) ₹315 (d) ₹105
31. 31.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹42 (d) ₹18
32. 32.If 9 pens cost ₹45, how much do 8 pens cost? (a) ₹40 (b) ₹360 (c) ₹45 (d) ₹44
33. 33.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹232 (b) ₹29 (c) ₹261 (d) ₹233
34. 34.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹189 (b) ₹135 (c) ₹243 (d) ₹27
35. 35.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹343 (c) ₹245 (d) ₹294
36. 36.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 3 days (d) 4 days
37. 37.If 3 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹65 (b) ₹60 (c) ₹180 (d) ₹24
38. 38.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 8 days (d) 10 days
39. 39.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 10 days (d) 16 days
40. 40.If 2 mangoes cost ₹8, how much do 6 mangoes cost? (a) ₹12 (b) ₹48 (c) ₹24 (d) ₹28

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