Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 974 · 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 notebooks cost ₹84, how much do 5 notebooks cost? (a) ₹420 (b) ₹72 (c) ₹82 (d) ₹60
2. 2.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹22 (b) ₹154 (c) ₹176 (d) ₹88
3. 3.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹70 (b) ₹71 (c) ₹105 (d) ₹35
4. 4.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹132 (b) ₹33 (c) ₹165 (d) ₹198
5. 5.If 9 pens cost ₹81, how much do 5 pens cost? (a) ₹54 (b) ₹77 (c) ₹45 (d) ₹405
6. 6.If 3 notebooks cost ₹33, how much do 4 notebooks cost? (a) ₹34 (b) ₹132 (c) ₹44 (d) ₹55
7. 7.If 8 mangoes cost ₹32, how much do 2 mangoes cost? (a) ₹12 (b) ₹64 (c) ₹8 (d) ₹26
8. 8.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 8 days (d) 7 days
9. 9.If 3 pens cost ₹18, how much do 4 pens cost? (a) ₹30 (b) ₹72 (c) ₹19 (d) ₹24
10. 10.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 7 days (c) 17 days (d) 6 days
11. 11.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 9 days
12. 12.If 5 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹39 (b) ₹22 (c) ₹180 (d) ₹36
13. 13.If 5 pens cost ₹120, how much do 8 pens cost? (a) ₹960 (b) ₹192 (c) ₹123 (d) ₹216
14. 14.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹90 (b) ₹30 (c) ₹120 (d) ₹60
15. 15.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 15 days (d) 14 days
16. 16.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 18 days (d) 11 days
17. 17.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹200 (b) ₹360 (c) ₹40 (d) ₹280
18. 18.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 22 days (d) 21 days
19. 19.If 6 pens cost ₹30, how much do 8 pens cost? (a) ₹40 (b) ₹32 (c) ₹240 (d) ₹45
20. 20.If 3 pens cost ₹12, how much do 5 pens cost? (a) ₹14 (b) ₹24 (c) ₹60 (d) ₹20
21. 21.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 12 days (d) 8 days
22. 22.₹282 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹47 (b) ₹282 (c) ₹141 (d) ₹235
23. 23.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹24 (b) ₹8 (c) ₹56 (d) ₹40
24. 24.If 2 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹60 (b) ₹36 (c) ₹30 (d) ₹15
25. 25.If 7 pens cost ₹98, how much do 5 pens cost? (a) ₹84 (b) ₹490 (c) ₹70 (d) ₹96
26. 26.If 4 pens cost ₹96, how much do 10 pens cost? (a) ₹102 (b) ₹960 (c) ₹264 (d) ₹240
27. 27.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
28. 28.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 1 day
29. 29.If 4 notebooks cost ₹32, how much do 11 notebooks cost? (a) ₹39 (b) ₹96 (c) ₹88 (d) ₹352
30. 30.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹168 (d) ₹210
31. 31.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 5 days
32. 32.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹8 (c) ₹20 (d) ₹16
33. 33.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 11 days (d) 13 days
34. 34.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹200 (d) ₹275
35. 35.If 7 pens cost ₹77, how much do 4 pens cost? (a) ₹44 (b) ₹55 (c) ₹308 (d) ₹74
36. 36.If 3 pens cost ₹63, how much do 5 pens cost? (a) ₹126 (b) ₹65 (c) ₹105 (d) ₹315
37. 37.If 3 pens cost ₹69, how much do 4 pens cost? (a) ₹70 (b) ₹92 (c) ₹115 (d) ₹276
38. 38.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹195 (b) ₹117 (c) ₹39 (d) ₹156
39. 39.If 8 kites cost ₹120, how much do 5 kites cost? (a) ₹117 (b) ₹75 (c) ₹600 (d) ₹90
40. 40.If 5 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹44 (b) ₹36 (c) ₹180 (d) ₹45

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