Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 821 · 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 9 kites cost ₹144, how much do 10 kites cost? (a) ₹176 (b) ₹160 (c) ₹145 (d) ₹1440
2. 2.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 9 days (d) 15 days
3. 3.If 6 notebooks cost ₹90, how much do 9 notebooks cost? (a) ₹150 (b) ₹93 (c) ₹135 (d) ₹810
4. 4.If 8 pens cost ₹32, how much do 10 pens cost? (a) ₹40 (b) ₹34 (c) ₹320 (d) ₹44
5. 5.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 17 days (d) 19 days
6. 6.If 8 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹36 (b) ₹27 (c) ₹33 (d) ₹264
7. 7.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 9 days (d) 15 days
8. 8.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹282 (d) ₹235
9. 9.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹23 (b) ₹139 (c) ₹161 (d) ₹138
10. 10.If 6 kites cost ₹120, how much do 3 kites cost? (a) ₹60 (b) ₹117 (c) ₹80 (d) ₹360
11. 11.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹66 (b) ₹55 (c) ₹11 (d) ₹44
12. 12.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 5 days (d) 7 days
13. 13.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 10 days
14. 14.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹260 (b) ₹200 (c) ₹320 (d) ₹40
15. 15.If 9 pens cost ₹171, how much do 2 pens cost? (a) ₹342 (b) ₹164 (c) ₹38 (d) ₹57
16. 16.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹231 (d) ₹297
17. 17.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 26 days (d) 15 days
18. 18.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 61 days (b) 9 days (c) 60 days (d) 21 days
19. 19.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 5 days
20. 20.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹39 (c) ₹52 (d) ₹13
21. 21.₹470 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹470 (b) ₹235 (c) ₹423 (d) ₹47
22. 22.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 6 days (d) 5 days
23. 23.₹90 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹9 (c) ₹45 (d) ₹81
24. 24.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹43 (b) ₹173 (c) ₹215 (d) ₹172
25. 25.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹96 (d) ₹112
26. 26.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹70 (d) ₹30
27. 27.If 7 notebooks cost ₹168, how much do 3 notebooks cost? (a) ₹96 (b) ₹504 (c) ₹164 (d) ₹72
28. 28.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹225 (b) ₹90 (c) ₹45 (d) ₹270
29. 29.If 3 mangoes cost ₹75, how much do 2 mangoes cost? (a) ₹74 (b) ₹75 (c) ₹150 (d) ₹50
30. 30.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 11 days (d) 14 days
31. 31.If 4 kites cost ₹52, how much do 10 kites cost? (a) ₹520 (b) ₹58 (c) ₹143 (d) ₹130
32. 32.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 2 days (d) 8 days
33. 33.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 31 days (c) 9 days (d) 30 days
34. 34.If 2 pens cost ₹34, how much do 12 pens cost? (a) ₹408 (b) ₹44 (c) ₹221 (d) ₹204
35. 35.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹75 (c) ₹15 (d) ₹90
36. 36.If 3 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹34 (b) ₹99 (c) ₹90 (d) ₹270
37. 37.If 2 kites cost ₹32, how much do 8 kites cost? (a) ₹128 (b) ₹144 (c) ₹38 (d) ₹256
38. 38.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹352 (b) ₹220 (c) ₹44 (d) ₹286
39. 39.If 4 mangoes cost ₹40, how much do 10 mangoes cost? (a) ₹100 (b) ₹110 (c) ₹46 (d) ₹400
40. 40.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days

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