Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 574 · 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. 1.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 11 days (d) 17 days
2. 2.If 4 notebooks cost ₹40, how much do 10 notebooks cost? (a) ₹100 (b) ₹400 (c) ₹46 (d) ₹110
3. 3.If 3 mangoes cost ₹66, how much do 6 mangoes cost? (a) ₹154 (b) ₹69 (c) ₹132 (d) ₹396
4. 4.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹119 (b) ₹136 (c) ₹17 (d) ₹68
5. 5.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹144 (d) ₹126
6. 6.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹55 (b) ₹77 (c) ₹99 (d) ₹11
7. 7.If 2 kites cost ₹48, how much do 3 kites cost? (a) ₹144 (b) ₹72 (c) ₹96 (d) ₹49
8. 8.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹144 (b) ₹96 (c) ₹72 (d) ₹49
9. 9.If 7 mangoes cost ₹56, how much do 8 mangoes cost? (a) ₹72 (b) ₹448 (c) ₹57 (d) ₹64
10. 10.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 5 days (d) 22 days
11. 11.If 3 pens cost ₹27, how much do 9 pens cost? (a) ₹33 (b) ₹81 (c) ₹243 (d) ₹90
12. 12.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹38 (b) ₹114 (c) ₹209 (d) ₹304
13. 13.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹30 (b) ₹165 (c) ₹60 (d) ₹270
14. 14.If 2 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹24 (b) ₹17 (c) ₹32 (d) ₹48
15. 15.If 2 kites cost ₹16, how much do 3 kites cost? (a) ₹48 (b) ₹32 (c) ₹17 (d) ₹24
16. 16.If 2 kites cost ₹18, how much do 10 kites cost? (a) ₹180 (b) ₹99 (c) ₹90 (d) ₹26
17. 17.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
18. 18.If 5 kites cost ₹95, how much do 7 kites cost? (a) ₹133 (b) ₹97 (c) ₹665 (d) ₹152
19. 19.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 4 days
20. 20.If 3 pens cost ₹66, how much do 12 pens cost? (a) ₹75 (b) ₹264 (c) ₹286 (d) ₹792
21. 21.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 9 days (d) 15 days
22. 22.If 4 pens cost ₹12, how much do 7 pens cost? (a) ₹24 (b) ₹15 (c) ₹21 (d) ₹84
23. 23.If 4 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹66 (b) ₹55 (c) ₹220 (d) ₹45
24. 24.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹34 (b) ₹221 (c) ₹170 (d) ₹272
25. 25.If 9 kites cost ₹27, how much do 10 kites cost? (a) ₹30 (b) ₹28 (c) ₹270 (d) ₹33
26. 26.If 2 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹220 (b) ₹110 (c) ₹47 (d) ₹132
27. 27.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 12 days (d) 6 days
28. 28.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹258 (c) ₹301 (d) ₹215
29. 29.If 6 kites cost ₹36, how much do 7 kites cost? (a) ₹37 (b) ₹252 (c) ₹42 (d) ₹48
30. 30.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 11 days (d) 7 days
31. 31.If 3 kites cost ₹18, how much do 2 kites cost? (a) ₹17 (b) ₹18 (c) ₹12 (d) ₹36
32. 32.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 7 days (d) 4 days
33. 33.₹170 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹85 (b) ₹170 (c) ₹153 (d) ₹17
34. 34.If 3 mangoes cost ₹51, how much do 2 mangoes cost? (a) ₹34 (b) ₹51 (c) ₹102 (d) ₹50
35. 35.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹175 (b) ₹315 (c) ₹35 (d) ₹280
36. 36.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 13 days (d) 11 days
37. 37.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 7 days (d) 39 days
38. 38.If 2 pens cost ₹44, how much do 9 pens cost? (a) ₹396 (b) ₹198 (c) ₹220 (d) ₹51
39. 39.If 5 pens cost ₹90, how much do 8 pens cost? (a) ₹720 (b) ₹162 (c) ₹144 (d) ₹93
40. 40.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹126 (b) ₹36 (c) ₹108 (d) ₹144

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