Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 667 · 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.If 2 mangoes cost ₹18, how much do 6 mangoes cost? (a) ₹108 (b) ₹22 (c) ₹63 (d) ₹54
2. 2.If 9 mangoes cost ₹216, how much do 6 mangoes cost? (a) ₹168 (b) ₹144 (c) ₹1296 (d) ₹213
3. 3.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 12 days (d) 10 days
4. 4.If 6 kites cost ₹84, how much do 3 kites cost? (a) ₹56 (b) ₹42 (c) ₹81 (d) ₹252
5. 5.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 7 days (d) 16 days
6. 6.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 10 days (d) 19 days
7. 7.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹40 (c) ₹20 (d) ₹60
8. 8.If 3 kites cost ₹33, how much do 2 kites cost? (a) ₹66 (b) ₹32 (c) ₹33 (d) ₹22
9. 9.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 28 days (c) 29 days (d) 13 days
10. 10.If 5 kites cost ₹45, how much do 2 kites cost? (a) ₹18 (b) ₹90 (c) ₹42 (d) ₹27
11. 11.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 16 days
12. 12.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 13 days (d) 9 days
13. 13.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 35 days (d) 36 days
14. 14.If 8 kites cost ₹128, how much do 10 kites cost? (a) ₹130 (b) ₹160 (c) ₹176 (d) ₹1280
15. 15.If 8 mangoes cost ₹24, how much do 3 mangoes cost? (a) ₹19 (b) ₹72 (c) ₹9 (d) ₹12
16. 16.₹414 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹92 (b) ₹322 (c) ₹207 (d) ₹46
17. 17.₹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
18. 18.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 1 day (c) 9 days (d) 3 days
19. 19.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹148 (b) ₹370 (c) ₹333 (d) ₹37
20. 20.If 5 pens cost ₹15, how much do 3 pens cost? (a) ₹13 (b) ₹12 (c) ₹45 (d) ₹9
21. 21.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹315 (c) ₹225 (d) ₹270
22. 22.If 2 kites cost ₹12, how much do 7 kites cost? (a) ₹84 (b) ₹48 (c) ₹42 (d) ₹17
23. 23.If 9 kites cost ₹126, how much do 2 kites cost? (a) ₹119 (b) ₹28 (c) ₹42 (d) ₹252
24. 24.₹329 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹235 (b) ₹188 (c) ₹141 (d) ₹47
25. 25.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹60 (d) ₹45
26. 26.If 7 kites cost ₹133, how much do 4 kites cost? (a) ₹95 (b) ₹130 (c) ₹76 (d) ₹532
27. 27.If 8 pens cost ₹112, how much do 5 pens cost? (a) ₹84 (b) ₹109 (c) ₹70 (d) ₹560
28. 28.If 9 mangoes cost ₹36, how much do 11 mangoes cost? (a) ₹396 (b) ₹48 (c) ₹44 (d) ₹38
29. 29.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹117 (d) ₹13
30. 30.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 19 days (d) 9 days
31. 31.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 10 days (d) 8 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) 5 days (c) 3 days (d) 4 days
33. 33.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹45 (c) ₹54 (d) ₹36
34. 34.If 9 notebooks cost ₹99, how much do 2 notebooks cost? (a) ₹92 (b) ₹33 (c) ₹198 (d) ₹22
35. 35.If 9 pens cost ₹189, how much do 12 pens cost? (a) ₹2268 (b) ₹252 (c) ₹192 (d) ₹273
36. 36.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 11 days (d) 10 days
37. 37.If 2 kites cost ₹30, how much do 5 kites cost? (a) ₹33 (b) ₹75 (c) ₹90 (d) ₹150
38. 38.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 21 days (d) 11 days
39. 39.If 4 pens cost ₹32, how much do 2 pens cost? (a) ₹24 (b) ₹64 (c) ₹16 (d) ₹30
40. 40.If 3 mangoes cost ₹66, how much do 7 mangoes cost? (a) ₹176 (b) ₹70 (c) ₹462 (d) ₹154

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