Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 288 · 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.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹88 (d) ₹77
2. 2.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹130 (b) ₹117 (c) ₹104 (d) ₹26
3. 3.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 9 days (d) 14 days
4. 4.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹252 (b) ₹42 (c) ₹210 (d) ₹294
5. 5.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 8 days
6. 6.If 9 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹42 (b) ₹119 (c) ₹28 (d) ₹252
7. 7.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹360 (d) ₹280
8. 8.If 5 kites cost ₹100, how much do 6 kites cost? (a) ₹600 (b) ₹140 (c) ₹120 (d) ₹101
9. 9.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹154 (b) ₹110 (c) ₹22 (d) ₹132
10. 10.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 48 days (d) 6 days
11. 11.3 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) 3 days (d) 2 days
12. 12.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹123 (d) ₹164
13. 13.If 7 mangoes cost ₹77, how much do 3 mangoes cost? (a) ₹231 (b) ₹33 (c) ₹73 (d) ₹44
14. 14.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 36 days (d) 35 days
15. 15.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹39 (b) ₹52 (c) ₹65 (d) ₹13
16. 16.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹51 (d) ₹17
17. 17.If 5 notebooks cost ₹25, how much do 12 notebooks cost? (a) ₹300 (b) ₹65 (c) ₹32 (d) ₹60
18. 18.If 6 kites cost ₹108, how much do 8 kites cost? (a) ₹864 (b) ₹144 (c) ₹162 (d) ₹110
19. 19.If 2 mangoes cost ₹16, how much do 4 mangoes cost? (a) ₹64 (b) ₹32 (c) ₹40 (d) ₹18
20. 20.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹135 (b) ₹315 (c) ₹45 (d) ₹225
21. 21.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 10 days (d) 2 days
22. 22.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 19 days (c) 14 days (d) 18 days
23. 23.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹95 (b) ₹77 (c) ₹76 (d) ₹19
24. 24.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 12 days
25. 25.₹156 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹156 (d) ₹130
26. 26.If 4 mangoes cost ₹68, how much do 3 mangoes cost? (a) ₹51 (b) ₹204 (c) ₹68 (d) ₹67
27. 27.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 19 days (c) 11 days (d) 21 days
28. 28.If 8 kites cost ₹160, how much do 4 kites cost? (a) ₹156 (b) ₹640 (c) ₹100 (d) ₹80
29. 29.If 9 mangoes cost ₹216, how much do 8 mangoes cost? (a) ₹1728 (b) ₹192 (c) ₹216 (d) ₹215
30. 30.₹250 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹25 (b) ₹250 (c) ₹225 (d) ₹125
31. 31.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 5 days (d) 20 days
32. 32.If 8 mangoes cost ₹40, how much do 10 mangoes cost? (a) ₹400 (b) ₹55 (c) ₹50 (d) ₹42
33. 33.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 9 days (d) 8 days
34. 34.₹329 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹141 (d) ₹235
35. 35.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 33 days (d) 7 days
36. 36.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹61 (c) ₹60 (d) ₹15
37. 37.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹18 (d) ₹54
38. 38.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 29 days (d) 28 days
39. 39.If 4 kites cost ₹44, how much do 5 kites cost? (a) ₹55 (b) ₹220 (c) ₹45 (d) ₹66
40. 40.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹88 (b) ₹66 (c) ₹45 (d) ₹132

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