Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 669 · 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 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 13 days (d) 9 days
2. 2.If 8 notebooks cost ₹176, how much do 12 notebooks cost? (a) ₹286 (b) ₹2112 (c) ₹264 (d) ₹180
3. 3.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 6 days
4. 4.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹420 (d) ₹378
5. 5.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹135 (d) ₹120
6. 6.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 19 days (d) 3 days
7. 7.If 9 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹37 (b) ₹40 (c) ₹44 (d) ₹360
8. 8.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹102 (d) ₹85
9. 9.If 4 notebooks cost ₹20, how much do 12 notebooks cost? (a) ₹28 (b) ₹60 (c) ₹65 (d) ₹240
10. 10.If 6 pens cost ₹96, how much do 9 pens cost? (a) ₹864 (b) ₹99 (c) ₹160 (d) ₹144
11. 11.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
12. 12.If 8 pens cost ₹88, how much do 10 pens cost? (a) ₹110 (b) ₹90 (c) ₹880 (d) ₹121
13. 13.If 7 notebooks cost ₹28, how much do 12 notebooks cost? (a) ₹52 (b) ₹336 (c) ₹48 (d) ₹33
14. 14.If 6 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹31 (b) ₹210 (c) ₹40 (d) ₹35
15. 15.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 7 days (d) 12 days
16. 16.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 15 days (d) 14 days
17. 17.If 6 kites cost ₹102, how much do 3 kites cost? (a) ₹306 (b) ₹68 (c) ₹99 (d) ₹51
18. 18.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 4 days (d) 49 days
19. 19.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 7 days (d) 13 days
20. 20.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹37 (b) ₹222 (c) ₹185 (d) ₹259
21. 21.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹48 (d) ₹96
22. 22.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 42 days (c) 43 days (d) 10 days
23. 23.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹88 (d) ₹154
24. 24.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 2 days (d) 10 days
25. 25.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹180 (c) ₹100 (d) ₹20
26. 26.If 2 notebooks cost ₹22, how much do 4 notebooks cost? (a) ₹44 (b) ₹55 (c) ₹88 (d) ₹24
27. 27.If 2 pens cost ₹26, how much do 4 pens cost? (a) ₹52 (b) ₹28 (c) ₹104 (d) ₹65
28. 28.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 21 days (b) 3 days (c) 48 days (d) 4 days
29. 29.If 8 pens cost ₹184, how much do 6 pens cost? (a) ₹182 (b) ₹161 (c) ₹138 (d) ₹1104
30. 30.If 5 pens cost ₹75, how much do 8 pens cost? (a) ₹600 (b) ₹135 (c) ₹120 (d) ₹78
31. 31.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 10 days (d) 16 days
32. 32.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 5 days (d) 3 days
33. 33.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹282 (b) ₹94 (c) ₹235 (d) ₹47
34. 34.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 14 days (c) 16 days (d) 2 days
35. 35.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹32 (b) ₹64 (c) ₹48 (d) ₹96
36. 36.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹180 (b) ₹216 (c) ₹252 (d) ₹36
37. 37.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹50 (b) ₹175 (c) ₹100 (d) ₹250
38. 38.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹126 (b) ₹99 (c) ₹72 (d) ₹18
39. 39.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹49 (b) ₹147 (c) ₹196 (d) ₹98
40. 40.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹231 (b) ₹294 (c) ₹42 (d) ₹168

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