Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 551 · 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. 1.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 11 days (d) 13 days
2. 2.If 6 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹42 (b) ₹48 (c) ₹37 (d) ₹252
3. 3.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 8 days
4. 4.If 8 kites cost ₹56, how much do 9 kites cost? (a) ₹504 (b) ₹57 (c) ₹70 (d) ₹63
5. 5.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 21 days (d) 13 days
6. 6.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹85 (d) ₹119
7. 7.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 5 days (d) 4 days
8. 8.If 6 mangoes cost ₹54, how much do 5 mangoes cost? (a) ₹270 (b) ₹53 (c) ₹54 (d) ₹45
9. 9.If 7 mangoes cost ₹119, how much do 9 mangoes cost? (a) ₹1071 (b) ₹153 (c) ₹121 (d) ₹170
10. 10.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 12 days (d) 16 days
11. 11.If 5 kites cost ₹55, how much do 2 kites cost? (a) ₹110 (b) ₹52 (c) ₹33 (d) ₹22
12. 12.If 7 pens cost ₹63, how much do 3 pens cost? (a) ₹59 (b) ₹36 (c) ₹27 (d) ₹189
13. 13.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 6 days (d) 8 days
14. 14.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 16 days (c) 22 days (d) 12 days
15. 15.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹34 (b) ₹68 (c) ₹102 (d) ₹136
16. 16.If 5 kites cost ₹120, how much do 10 kites cost? (a) ₹125 (b) ₹264 (c) ₹240 (d) ₹1200
17. 17.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹117 (d) ₹91
18. 18.If 6 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹84 (b) ₹462 (c) ₹77 (d) ₹47
19. 19.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 64 days (d) 63 days
20. 20.If 5 kites cost ₹45, how much do 10 kites cost? (a) ₹50 (b) ₹450 (c) ₹99 (d) ₹90
21. 21.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹180 (d) ₹160
22. 22.If 4 notebooks cost ₹20, how much do 2 notebooks cost? (a) ₹18 (b) ₹15 (c) ₹10 (d) ₹40
23. 23.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹430 (b) ₹215 (c) ₹43 (d) ₹387
24. 24.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 19 days
25. 25.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 14 days (c) 10 days (d) 6 days
26. 26.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 3 days (d) 10 days
27. 27.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹400 (c) ₹325 (d) ₹250
28. 28.If 4 pens cost ₹20, how much do 3 pens cost? (a) ₹19 (b) ₹15 (c) ₹60 (d) ₹20
29. 29.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 5 days (d) 4 days
30. 30.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹172 (b) ₹215 (c) ₹129 (d) ₹43
31. 31.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹66 (b) ₹24 (c) ₹108 (d) ₹12
32. 32.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹80 (d) ₹112
33. 33.If 4 kites cost ₹32, how much do 8 kites cost? (a) ₹64 (b) ₹36 (c) ₹72 (d) ₹256
34. 34.If 8 kites cost ₹72, how much do 9 kites cost? (a) ₹90 (b) ₹648 (c) ₹81 (d) ₹73
35. 35.If 5 mangoes cost ₹85, how much do 8 mangoes cost? (a) ₹136 (b) ₹88 (c) ₹153 (d) ₹680
36. 36.If 8 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹48 (b) ₹36 (c) ₹52 (d) ₹384
37. 37.₹63 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹55 (b) ₹54 (c) ₹63 (d) ₹9
38. 38.₹170 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹85 (b) ₹119 (c) ₹17 (d) ₹51
39. 39.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹369 (b) ₹205 (c) ₹41 (d) ₹328
40. 40.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 24 days (d) 23 days

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