Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 248 · 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.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹66 (b) ₹77 (c) ₹88 (d) ₹22
2. 2.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 5 days
3. 3.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹27 (c) ₹19 (d) ₹9
4. 4.If 3 mangoes cost ₹51, how much do 5 mangoes cost? (a) ₹255 (b) ₹85 (c) ₹102 (d) ₹53
5. 5.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 6 days (d) 5 days
6. 6.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 8 days
7. 7.If 4 kites cost ₹12, how much do 3 kites cost? (a) ₹12 (b) ₹36 (c) ₹11 (d) ₹9
8. 8.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹184 (d) ₹253
9. 9.If 7 kites cost ₹140, how much do 3 kites cost? (a) ₹80 (b) ₹420 (c) ₹136 (d) ₹60
10. 10.If 3 notebooks cost ₹69, how much do 9 notebooks cost? (a) ₹207 (b) ₹75 (c) ₹621 (d) ₹230
11. 11.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 3 days (d) 4 days
12. 12.If 5 notebooks cost ₹110, how much do 2 notebooks cost? (a) ₹107 (b) ₹220 (c) ₹44 (d) ₹66
13. 13.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹203 (b) ₹116 (c) ₹29 (d) ₹232
14. 14.If 3 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹210 (b) ₹70 (c) ₹77 (d) ₹28
15. 15.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹184 (b) ₹92 (c) ₹161 (d) ₹23
16. 16.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹15 (b) ₹20 (c) ₹25 (d) ₹5
17. 17.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 1 day (d) 22 days
18. 18.If 6 pens cost ₹90, how much do 7 pens cost? (a) ₹630 (b) ₹105 (c) ₹120 (d) ₹91
19. 19.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 3 days (d) 4 days
20. 20.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
21. 21.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹234 (d) ₹273
22. 22.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹342 (b) ₹190 (c) ₹38 (d) ₹266
23. 23.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 11 days (d) 16 days
24. 24.If 7 pens cost ₹84, how much do 12 pens cost? (a) ₹1008 (b) ₹89 (c) ₹156 (d) ₹144
25. 25.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹248 (b) ₹124 (c) ₹217 (d) ₹31
26. 26.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 5 days (d) 9 days
27. 27.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 18 days (d) 28 days
28. 28.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 19 days (d) 12 days
29. 29.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 13 days (d) 3 days
30. 30.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹156 (b) ₹312 (c) ₹273 (d) ₹39
31. 31.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 7 days
32. 32.If 4 kites cost ₹32, how much do 9 kites cost? (a) ₹288 (b) ₹72 (c) ₹37 (d) ₹80
33. 33.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹282 (b) ₹188 (c) ₹235 (d) ₹47
34. 34.If 2 pens cost ₹32, how much do 11 pens cost? (a) ₹41 (b) ₹192 (c) ₹176 (d) ₹352
35. 35.If 4 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹68 (b) ₹180 (c) ₹195 (d) ₹720
36. 36.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 5 days (d) 6 days
37. 37.If 4 notebooks cost ₹68, how much do 5 notebooks cost? (a) ₹69 (b) ₹85 (c) ₹102 (d) ₹340
38. 38.If 7 pens cost ₹140, how much do 6 pens cost? (a) ₹140 (b) ₹139 (c) ₹120 (d) ₹840
39. 39.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹148 (d) ₹185
40. 40.If 3 pens cost ₹21, how much do 10 pens cost? (a) ₹28 (b) ₹77 (c) ₹210 (d) ₹70

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