Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 439 · 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. 1.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 5 days (c) 13 days (d) 21 days
2. 2.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹37 (b) ₹74 (c) ₹111 (d) ₹148
3. 3.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹126 (d) ₹99
4. 4.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 10 days (d) 13 days
5. 5.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 9 days
6. 6.If 6 pens cost ₹90, how much do 4 pens cost? (a) ₹360 (b) ₹88 (c) ₹60 (d) ₹75
7. 7.If 8 kites cost ₹88, how much do 12 kites cost? (a) ₹1056 (b) ₹92 (c) ₹132 (d) ₹143
8. 8.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 3 days (d) 12 days
9. 9.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 10 days (d) 2 days
10. 10.If 6 kites cost ₹30, how much do 2 kites cost? (a) ₹60 (b) ₹26 (c) ₹15 (d) ₹10
11. 11.If 2 notebooks cost ₹34, how much do 3 notebooks cost? (a) ₹51 (b) ₹35 (c) ₹68 (d) ₹102
12. 12.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹129 (b) ₹87 (c) ₹86 (d) ₹43
13. 13.If 3 notebooks cost ₹66, how much do 2 notebooks cost? (a) ₹132 (b) ₹44 (c) ₹65 (d) ₹66
14. 14.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹133 (b) ₹165 (c) ₹33 (d) ₹132
15. 15.If 2 kites cost ₹48, how much do 12 kites cost? (a) ₹576 (b) ₹312 (c) ₹288 (d) ₹58
16. 16.If 3 mangoes cost ₹69, how much do 11 mangoes cost? (a) ₹276 (b) ₹77 (c) ₹253 (d) ₹759
17. 17.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹172 (b) ₹43 (c) ₹215 (d) ₹173
18. 18.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 13 days (d) 5 days
19. 19.If 4 notebooks cost ₹76, how much do 5 notebooks cost? (a) ₹95 (b) ₹380 (c) ₹114 (d) ₹77
20. 20.₹235 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹235 (b) ₹188 (c) ₹47 (d) ₹189
21. 21.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹129 (b) ₹43 (c) ₹387 (d) ₹344
22. 22.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹25 (c) ₹21 (d) ₹5
23. 23.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹81 (d) ₹54
24. 24.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 17 days (d) 18 days
25. 25.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹117 (b) ₹13 (c) ₹104 (d) ₹105
26. 26.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹232 (b) ₹29 (c) ₹116 (d) ₹203
27. 27.If 5 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹210 (b) ₹48 (c) ₹32 (d) ₹42
28. 28.If 4 mangoes cost ₹64, how much do 9 mangoes cost? (a) ₹576 (b) ₹144 (c) ₹160 (d) ₹69
29. 29.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 10 days (d) 9 days
30. 30.If 4 pens cost ₹80, how much do 5 pens cost? (a) ₹120 (b) ₹100 (c) ₹81 (d) ₹400
31. 31.If 2 pens cost ₹8, how much do 4 pens cost? (a) ₹10 (b) ₹16 (c) ₹32 (d) ₹20
32. 32.If 8 mangoes cost ₹32, how much do 10 mangoes cost? (a) ₹44 (b) ₹34 (c) ₹40 (d) ₹320
33. 33.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 9 days (d) 49 days
34. 34.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 2 days (d) 3 days
35. 35.If 4 notebooks cost ₹60, how much do 2 notebooks cost? (a) ₹58 (b) ₹30 (c) ₹45 (d) ₹120
36. 36.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 6 days (d) 21 days
37. 37.If 3 pens cost ₹18, how much do 9 pens cost? (a) ₹60 (b) ₹54 (c) ₹24 (d) ₹162
38. 38.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 2 days (d) 3 days
39. 39.If 8 pens cost ₹96, how much do 6 pens cost? (a) ₹72 (b) ₹576 (c) ₹94 (d) ₹84
40. 40.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹126 (d) ₹108

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