Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 53 · 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. 1.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 13 days (c) 9 days (d) 22 days
2. 2.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹110 (b) ₹11 (c) ₹55 (d) ₹99
3. 3.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹35 (b) ₹63 (c) ₹7 (d) ₹70
4. 4.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹133 (b) ₹114 (c) ₹38 (d) ₹152
5. 5.If 4 notebooks cost ₹32, how much do 6 notebooks cost? (a) ₹48 (b) ₹34 (c) ₹192 (d) ₹56
6. 6.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 16 days (d) 9 days
7. 7.If 8 kites cost ₹200, how much do 5 kites cost? (a) ₹1000 (b) ₹197 (c) ₹125 (d) ₹150
8. 8.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 12 days (d) 18 days
9. 9.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹112 (d) ₹80
10. 10.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 11 days
11. 11.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 6 days (d) 5 days
12. 12.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 3 days (d) 2 days
13. 13.If 7 notebooks cost ₹42, how much do 2 notebooks cost? (a) ₹84 (b) ₹12 (c) ₹37 (d) ₹18
14. 14.If 9 kites cost ₹153, how much do 2 kites cost? (a) ₹306 (b) ₹34 (c) ₹51 (d) ₹146
15. 15.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 11 days (c) 30 days (d) 19 days
16. 16.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹120 (c) ₹200 (d) ₹280
17. 17.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 3 days
18. 18.If 9 mangoes cost ₹207, how much do 10 mangoes cost? (a) ₹230 (b) ₹2070 (c) ₹253 (d) ₹208
19. 19.If 6 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹36 (b) ₹51 (c) ₹162 (d) ₹27
20. 20.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 6 days (d) 7 days
21. 21.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 9 days (d) 25 days
22. 22.If 5 mangoes cost ₹125, how much do 6 mangoes cost? (a) ₹175 (b) ₹150 (c) ₹126 (d) ₹750
23. 23.₹270 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹135 (b) ₹240 (c) ₹30 (d) ₹270
24. 24.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 2 days
25. 25.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 24 days (d) 17 days
26. 26.If 3 kites cost ₹9, how much do 6 kites cost? (a) ₹18 (b) ₹21 (c) ₹12 (d) ₹54
27. 27.If 6 mangoes cost ₹84, how much do 12 mangoes cost? (a) ₹168 (b) ₹90 (c) ₹1008 (d) ₹182
28. 28.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 31 days (c) 30 days (d) 4 days
29. 29.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹140 (b) ₹35 (c) ₹350 (d) ₹315
30. 30.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 28 days (d) 27 days
31. 31.If 8 kites cost ₹104, how much do 10 kites cost? (a) ₹1040 (b) ₹143 (c) ₹130 (d) ₹106
32. 32.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 39 days (d) 7 days
33. 33.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 12 days (c) 30 days (d) 18 days
34. 34.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 2 days (d) 3 days
35. 35.If 6 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹53 (b) ₹96 (c) ₹88 (d) ₹528
36. 36.If 3 kites cost ₹39, how much do 6 kites cost? (a) ₹42 (b) ₹91 (c) ₹234 (d) ₹78
37. 37.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 6 days
38. 38.If 4 pens cost ₹84, how much do 6 pens cost? (a) ₹147 (b) ₹126 (c) ₹504 (d) ₹86
39. 39.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 5 days (d) 4 days
40. 40.If 9 pens cost ₹180, how much do 2 pens cost? (a) ₹360 (b) ₹173 (c) ₹40 (d) ₹60

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