Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 428 · 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.If 5 pens cost ₹60, how much do 7 pens cost? (a) ₹96 (b) ₹420 (c) ₹84 (d) ₹62
2. 2.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
3. 3.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹69 (d) ₹92
4. 4.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 4 days (d) 5 days
5. 5.If 8 pens cost ₹104, how much do 6 pens cost? (a) ₹102 (b) ₹78 (c) ₹624 (d) ₹91
6. 6.5 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) 3 days (d) 2 days
7. 7.₹30 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹15 (b) ₹5 (c) ₹30 (d) ₹25
8. 8.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 13 days (d) 28 days
9. 9.If 6 notebooks cost ₹144, how much do 12 notebooks cost? (a) ₹288 (b) ₹312 (c) ₹150 (d) ₹1728
10. 10.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 1 day (d) 3 days
11. 11.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
12. 12.If 4 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹15 (b) ₹21 (c) ₹84 (d) ₹24
13. 13.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 12 days (d) 8 days
14. 14.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹15 (c) ₹10 (d) ₹5
15. 15.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹56 (d) ₹48
16. 16.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹35 (d) ₹40
17. 17.₹495 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹450 (b) ₹405 (c) ₹90 (d) ₹45
18. 18.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹132 (b) ₹44 (c) ₹88 (d) ₹110
19. 19.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹8 (d) ₹40
20. 20.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
21. 21.If 2 mangoes cost ₹10, how much do 5 mangoes cost? (a) ₹50 (b) ₹25 (c) ₹13 (d) ₹30
22. 22.₹246 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹123 (b) ₹41 (c) ₹246 (d) ₹205
23. 23.6 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
24. 24.If 7 pens cost ₹154, how much do 2 pens cost? (a) ₹66 (b) ₹308 (c) ₹44 (d) ₹149
25. 25.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹24 (b) ₹54 (c) ₹84 (d) ₹12
26. 26.If 2 notebooks cost ₹22, how much do 6 notebooks cost? (a) ₹66 (b) ₹26 (c) ₹132 (d) ₹77
27. 27.If 2 kites cost ₹22, how much do 3 kites cost? (a) ₹66 (b) ₹33 (c) ₹23 (d) ₹44
28. 28.If 9 notebooks cost ₹153, how much do 10 notebooks cost? (a) ₹187 (b) ₹154 (c) ₹170 (d) ₹1530
29. 29.If 5 mangoes cost ₹80, how much do 8 mangoes cost? (a) ₹144 (b) ₹83 (c) ₹128 (d) ₹640
30. 30.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹27 (b) ₹163 (c) ₹162 (d) ₹189
31. 31.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 5 days
32. 32.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
33. 33.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹144 (b) ₹16 (c) ₹32 (d) ₹88
34. 34.₹245 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹49 (b) ₹197 (c) ₹196 (d) ₹245
35. 35.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 22 days (d) 21 days
36. 36.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 13 days (d) 12 days
37. 37.₹230 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹115 (b) ₹46 (c) ₹230 (d) ₹184
38. 38.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 11 days (c) 19 days (d) 36 days
39. 39.If 2 mangoes cost ₹30, how much do 11 mangoes cost? (a) ₹39 (b) ₹330 (c) ₹165 (d) ₹180
40. 40.If 2 notebooks cost ₹50, how much do 11 notebooks cost? (a) ₹550 (b) ₹300 (c) ₹59 (d) ₹275

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