Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 577 · 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 ₹144, how much do 5 notebooks cost? (a) ₹141 (b) ₹108 (c) ₹90 (d) ₹720
2. 2.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 8 days (d) 6 days
3. 3.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 1 day (d) 17 days
4. 4.If 6 mangoes cost ₹114, how much do 7 mangoes cost? (a) ₹798 (b) ₹115 (c) ₹152 (d) ₹133
5. 5.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹30 (d) ₹40
6. 6.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹50 (b) ₹275 (c) ₹350 (d) ₹200
7. 7.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹28 (c) ₹14 (d) ₹7
8. 8.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 4 days (d) 3 days
9. 9.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹368 (b) ₹230 (c) ₹299 (d) ₹46
10. 10.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹78 (b) ₹130 (c) ₹182 (d) ₹26
11. 11.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹30 (d) ₹10
12. 12.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹72 (b) ₹8 (c) ₹40 (d) ₹56
13. 13.If 6 pens cost ₹78, how much do 2 pens cost? (a) ₹39 (b) ₹156 (c) ₹26 (d) ₹74
14. 14.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 18 days (d) 11 days
15. 15.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹24 (b) ₹156 (c) ₹192 (d) ₹120
16. 16.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 40 days (d) 39 days
17. 17.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 20 days (c) 8 days (d) 7 days
18. 18.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹325 (b) ₹450 (c) ₹200 (d) ₹50
19. 19.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 23 days (d) 9 days
20. 20.If 7 kites cost ₹49, how much do 3 kites cost? (a) ₹147 (b) ₹21 (c) ₹45 (d) ₹28
21. 21.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 9 days (d) 5 days
22. 22.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹18 (b) ₹63 (c) ₹108 (d) ₹126
23. 23.If 4 kites cost ₹24, how much do 12 kites cost? (a) ₹288 (b) ₹72 (c) ₹32 (d) ₹78
24. 24.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 11 days (d) 7 days
25. 25.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹51 (d) ₹85
26. 26.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹48 (b) ₹432 (c) ₹240 (d) ₹336
27. 27.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 14 days
28. 28.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 8 days (d) 9 days
29. 29.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 1 day (d) 10 days
30. 30.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 12 days
31. 31.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 21 days (c) 63 days (d) 7 days
32. 32.If 4 pens cost ₹88, how much do 8 pens cost? (a) ₹176 (b) ₹704 (c) ₹92 (d) ₹198
33. 33.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 10 days (c) 42 days (d) 18 days
34. 34.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹210 (b) ₹378 (c) ₹420 (d) ₹42
35. 35.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹95 (d) ₹133
36. 36.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 28 days (d) 7 days
37. 37.If 8 pens cost ₹24, how much do 2 pens cost? (a) ₹18 (b) ₹6 (c) ₹48 (d) ₹9
38. 38.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 9 days (d) 10 days
39. 39.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
40. 40.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹8 (b) ₹72 (c) ₹36 (d) ₹64

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