Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 693 · 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. 1.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 9 days
2. 2.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 9 days (d) 3 days
3. 3.If 2 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹132 (b) ₹220 (c) ₹47 (d) ₹110
4. 4.If 7 mangoes cost ₹21, how much do 5 mangoes cost? (a) ₹19 (b) ₹105 (c) ₹15 (d) ₹18
5. 5.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 45 days (d) 44 days
6. 6.If 3 pens cost ₹12, how much do 2 pens cost? (a) ₹24 (b) ₹12 (c) ₹11 (d) ₹8
7. 7.If 5 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹34 (b) ₹140 (c) ₹35 (d) ₹28
8. 8.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹184 (b) ₹253 (c) ₹46 (d) ₹322
9. 9.If 7 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹140 (b) ₹24 (c) ₹26 (d) ₹20
10. 10.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹235 (d) ₹282
11. 11.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹24 (d) ₹48
12. 12.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹211 (b) ₹245 (c) ₹210 (d) ₹35
13. 13.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹273 (d) ₹234
14. 14.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 14 days (d) 13 days
15. 15.₹280 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹140 (b) ₹80 (c) ₹40 (d) ₹200
16. 16.₹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
17. 17.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
18. 18.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 7 days (d) 8 days
19. 19.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 8 days
20. 20.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹54 (d) ₹55
21. 21.If 4 pens cost ₹20, how much do 8 pens cost? (a) ₹24 (b) ₹160 (c) ₹45 (d) ₹40
22. 22.If 6 mangoes cost ₹48, how much do 7 mangoes cost? (a) ₹56 (b) ₹49 (c) ₹336 (d) ₹64
23. 23.₹155 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹125 (b) ₹155 (c) ₹124 (d) ₹31
24. 24.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 8 days
25. 25.If 5 pens cost ₹80, how much do 3 pens cost? (a) ₹48 (b) ₹240 (c) ₹64 (d) ₹78
26. 26.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹282 (b) ₹47 (c) ₹235 (d) ₹188
27. 27.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹37 (b) ₹259 (c) ₹111 (d) ₹185
28. 28.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 7 days (d) 17 days
29. 29.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 11 days (d) 19 days
30. 30.If 3 notebooks cost ₹66, how much do 8 notebooks cost? (a) ₹528 (b) ₹71 (c) ₹176 (d) ₹198
31. 31.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 10 days (d) 3 days
32. 32.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
33. 33.If 8 kites cost ₹200, how much do 2 kites cost? (a) ₹75 (b) ₹400 (c) ₹194 (d) ₹50
34. 34.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 15 days (d) 13 days
35. 35.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹185 (b) ₹149 (c) ₹148 (d) ₹37
36. 36.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹20 (c) ₹25 (d) ₹5
37. 37.If 3 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹96 (b) ₹288 (c) ₹120 (d) ₹73
38. 38.If 8 kites cost ₹24, how much do 5 kites cost? (a) ₹21 (b) ₹120 (c) ₹15 (d) ₹18
39. 39.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 1 day (d) 2 days
40. 40.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 11 days (d) 17 days

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