Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 37 · 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. 1.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 10 days (c) 41 days (d) 20 days
2. 2.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹50 (c) ₹250 (d) ₹100
3. 3.If 6 notebooks cost ₹66, how much do 12 notebooks cost? (a) ₹143 (b) ₹132 (c) ₹72 (d) ₹792
4. 4.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹180 (b) ₹405 (c) ₹45 (d) ₹450
5. 5.If 4 pens cost ₹36, how much do 5 pens cost? (a) ₹180 (b) ₹45 (c) ₹37 (d) ₹54
6. 6.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 5 days
7. 7.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹200 (b) ₹320 (c) ₹40 (d) ₹260
8. 8.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹99 (b) ₹147 (c) ₹49 (d) ₹98
9. 9.If 2 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹40 (b) ₹22 (c) ₹80 (d) ₹50
10. 10.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 10 days (c) 43 days (d) 18 days
11. 11.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 16 days (d) 11 days
12. 12.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 9 days (d) 14 days
13. 13.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹301 (b) ₹43 (c) ₹344 (d) ₹172
14. 14.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹414 (b) ₹322 (c) ₹230 (d) ₹46
15. 15.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 3 days (d) 10 days
16. 16.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 28 days (d) 3 days
17. 17.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹40 (d) ₹10
18. 18.If 2 mangoes cost ₹10, how much do 12 mangoes cost? (a) ₹120 (b) ₹60 (c) ₹65 (d) ₹20
19. 19.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹215 (d) ₹258
20. 20.If 3 pens cost ₹63, how much do 4 pens cost? (a) ₹84 (b) ₹105 (c) ₹64 (d) ₹252
21. 21.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹88 (b) ₹48 (c) ₹16 (d) ₹128
22. 22.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹25 (b) ₹175 (c) ₹150 (d) ₹151
23. 23.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹62 (b) ₹124 (c) ₹93 (d) ₹31
24. 24.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 19 days
25. 25.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 11 days
26. 26.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹8 (d) ₹12
27. 27.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 16 days (d) 28 days
28. 28.If 2 mangoes cost ₹14, how much do 3 mangoes cost? (a) ₹42 (b) ₹28 (c) ₹21 (d) ₹15
29. 29.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹80 (c) ₹10 (d) ₹65
30. 30.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹100 (b) ₹75 (c) ₹25 (d) ₹50
31. 31.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹272 (b) ₹170 (c) ₹34 (d) ₹221
32. 32.If 5 kites cost ₹15, how much do 3 kites cost? (a) ₹12 (b) ₹45 (c) ₹9 (d) ₹13
33. 33.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 22 days (d) 21 days
34. 34.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹48 (b) ₹264 (c) ₹240 (d) ₹288
35. 35.If 7 kites cost ₹63, how much do 3 kites cost? (a) ₹36 (b) ₹27 (c) ₹189 (d) ₹59
36. 36.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
37. 37.₹470 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹423 (b) ₹235 (c) ₹47 (d) ₹470
38. 38.If 3 mangoes cost ₹24, how much do 12 mangoes cost? (a) ₹288 (b) ₹33 (c) ₹104 (d) ₹96
39. 39.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 7 days (d) 4 days
40. 40.If 3 kites cost ₹63, how much do 5 kites cost? (a) ₹105 (b) ₹126 (c) ₹315 (d) ₹65

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