Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 805 · 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 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹100 (b) ₹90 (c) ₹81 (d) ₹720
2. 2.If 6 notebooks cost ₹30, how much do 8 notebooks cost? (a) ₹40 (b) ₹45 (c) ₹32 (d) ₹240
3. 3.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹58 (d) ₹59
4. 4.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹18 (b) ₹126 (c) ₹162 (d) ₹90
5. 5.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 7 days (d) 28 days
6. 6.₹297 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹265 (b) ₹264 (c) ₹33 (d) ₹297
7. 7.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 2 days
8. 8.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 4 days (d) 6 days
9. 9.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 7 days
10. 10.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 12 days (d) 7 days
11. 11.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 12 days (d) 4 days
12. 12.If 5 kites cost ₹65, how much do 2 kites cost? (a) ₹39 (b) ₹62 (c) ₹26 (d) ₹130
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.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹21 (d) ₹42
15. 15.If 9 pens cost ₹180, how much do 4 pens cost? (a) ₹175 (b) ₹100 (c) ₹80 (d) ₹720
16. 16.If 3 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹31 (b) ₹40 (c) ₹50 (d) ₹120
17. 17.If 3 kites cost ₹45, how much do 6 kites cost? (a) ₹90 (b) ₹48 (c) ₹105 (d) ₹270
18. 18.If 8 kites cost ₹104, how much do 6 kites cost? (a) ₹624 (b) ₹102 (c) ₹78 (d) ₹91
19. 19.If 3 mangoes cost ₹27, how much do 10 mangoes cost? (a) ₹34 (b) ₹90 (c) ₹270 (d) ₹99
20. 20.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 15 days (d) 27 days
21. 21.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹184 (d) ₹161
22. 22.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 9 days (d) 16 days
23. 23.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹182 (d) ₹156
24. 24.₹150 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹75 (b) ₹125 (c) ₹150 (d) ₹25
25. 25.If 9 kites cost ₹153, how much do 6 kites cost? (a) ₹102 (b) ₹119 (c) ₹150 (d) ₹918
26. 26.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 14 days (b) 7 days (c) 8 days (d) 9 days
27. 27.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 13 days (d) 16 days
28. 28.If 6 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹432 (b) ₹72 (c) ₹56 (d) ₹81
29. 29.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 23 days (d) 13 days
30. 30.If 3 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹55 (b) ₹90 (c) ₹72 (d) ₹216
31. 31.If 8 notebooks cost ₹200, how much do 2 notebooks cost? (a) ₹400 (b) ₹75 (c) ₹50 (d) ₹194
32. 32.If 2 mangoes cost ₹16, how much do 7 mangoes cost? (a) ₹56 (b) ₹64 (c) ₹112 (d) ₹21
33. 33.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 7 days (d) 11 days
34. 34.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹98 (b) ₹441 (c) ₹490 (d) ₹49
35. 35.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
36. 36.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹253 (b) ₹230 (c) ₹46 (d) ₹276
37. 37.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 25 days (c) 13 days (d) 4 days
38. 38.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 6 days (d) 9 days
39. 39.7 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) 35 days (d) 36 days
40. 40.If 6 notebooks cost ₹66, how much do 5 notebooks cost? (a) ₹65 (b) ₹330 (c) ₹66 (d) ₹55

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