Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 204 · 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 7 kites cost ₹168, how much do 8 kites cost? (a) ₹1344 (b) ₹192 (c) ₹169 (d) ₹216
2. 2.If 7 mangoes cost ₹126, how much do 6 mangoes cost? (a) ₹126 (b) ₹756 (c) ₹108 (d) ₹125
3. 3.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹88 (b) ₹110 (c) ₹132 (d) ₹44
4. 4.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹36 (c) ₹16 (d) ₹8
5. 5.If 2 pens cost ₹38, how much do 11 pens cost? (a) ₹209 (b) ₹418 (c) ₹228 (d) ₹47
6. 6.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹18 (c) ₹36 (d) ₹54
7. 7.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹144 (b) ₹90 (c) ₹72 (d) ₹38
8. 8.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 7 days (d) 9 days
9. 9.If 7 mangoes cost ₹84, how much do 3 mangoes cost? (a) ₹252 (b) ₹36 (c) ₹80 (d) ₹48
10. 10.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹215 (b) ₹86 (c) ₹43 (d) ₹258
11. 11.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 4 days (c) 41 days (d) 16 days
12. 12.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 8 days (c) 12 days (d) 5 days
13. 13.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 6 days (d) 16 days
14. 14.If 3 notebooks cost ₹21, how much do 5 notebooks cost? (a) ₹23 (b) ₹42 (c) ₹105 (d) ₹35
15. 15.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹396 (b) ₹440 (c) ₹220 (d) ₹44
16. 16.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 6 days (d) 4 days
17. 17.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹231 (b) ₹42 (c) ₹84 (d) ₹378
18. 18.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 15 days (d) 9 days
19. 19.If 5 pens cost ₹20, how much do 4 pens cost? (a) ₹19 (b) ₹80 (c) ₹16 (d) ₹20
20. 20.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 4 days (d) 16 days
21. 21.If 7 pens cost ₹42, how much do 3 pens cost? (a) ₹38 (b) ₹126 (c) ₹18 (d) ₹24
22. 22.If 3 pens cost ₹51, how much do 12 pens cost? (a) ₹60 (b) ₹612 (c) ₹204 (d) ₹221
23. 23.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 11 days (d) 10 days
24. 24.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹78 (d) ₹13
25. 25.If 9 pens cost ₹81, how much do 8 pens cost? (a) ₹80 (b) ₹72 (c) ₹648 (d) ₹81
26. 26.If 6 pens cost ₹102, how much do 12 pens cost? (a) ₹108 (b) ₹1224 (c) ₹221 (d) ₹204
27. 27.If 3 mangoes cost ₹48, how much do 6 mangoes cost? (a) ₹288 (b) ₹51 (c) ₹112 (d) ₹96
28. 28.If 5 pens cost ₹60, how much do 6 pens cost? (a) ₹72 (b) ₹84 (c) ₹61 (d) ₹360
29. 29.If 5 pens cost ₹55, how much do 6 pens cost? (a) ₹330 (b) ₹77 (c) ₹56 (d) ₹66
30. 30.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹90 (c) ₹18 (d) ₹54
31. 31.If 5 pens cost ₹25, how much do 3 pens cost? (a) ₹15 (b) ₹23 (c) ₹75 (d) ₹20
32. 32.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 16 days (d) 15 days
33. 33.If 6 kites cost ₹78, how much do 7 kites cost? (a) ₹79 (b) ₹546 (c) ₹104 (d) ₹91
34. 34.If 3 pens cost ₹30, how much do 10 pens cost? (a) ₹110 (b) ₹300 (c) ₹100 (d) ₹37
35. 35.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 10 days (d) 9 days
36. 36.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹336 (b) ₹96 (c) ₹48 (d) ₹216
37. 37.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹148 (d) ₹296
38. 38.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 8 days (d) 7 days
39. 39.If 5 pens cost ₹95, how much do 11 pens cost? (a) ₹228 (b) ₹101 (c) ₹1045 (d) ₹209
40. 40.If 2 notebooks cost ₹12, how much do 3 notebooks cost? (a) ₹36 (b) ₹24 (c) ₹13 (d) ₹18

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