Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 873 · 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. 1.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 18 days (d) 15 days
2. 2.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹99 (d) ₹55
3. 3.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 9 days (d) 7 days
4. 4.6 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) 18 days (d) 42 days
5. 5.If 8 kites cost ₹136, how much do 2 kites cost? (a) ₹272 (b) ₹130 (c) ₹51 (d) ₹34
6. 6.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹132 (b) ₹133 (c) ₹33 (d) ₹165
7. 7.If 2 mangoes cost ₹20, how much do 4 mangoes cost? (a) ₹50 (b) ₹40 (c) ₹22 (d) ₹80
8. 8.If 6 kites cost ₹48, how much do 11 kites cost? (a) ₹528 (b) ₹88 (c) ₹96 (d) ₹53
9. 9.If 5 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹20 (b) ₹16 (c) ₹19 (d) ₹80
10. 10.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 9 days (d) 11 days
11. 11.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹405 (c) ₹360 (d) ₹225
12. 12.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹230 (b) ₹322 (c) ₹276 (d) ₹46
13. 13.If 4 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹25 (b) ₹30 (c) ₹36 (d) ₹120
14. 14.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 18 days (d) 36 days
15. 15.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 13 days (d) 11 days
16. 16.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹144 (d) ₹336
17. 17.If 6 kites cost ₹150, how much do 7 kites cost? (a) ₹175 (b) ₹200 (c) ₹151 (d) ₹1050
18. 18.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 35 days (c) 36 days (d) 15 days
19. 19.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 29 days (c) 3 days (d) 28 days
20. 20.If 8 kites cost ₹168, how much do 10 kites cost? (a) ₹170 (b) ₹231 (c) ₹210 (d) ₹1680
21. 21.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹32 (b) ₹44 (c) ₹56 (d) ₹8
22. 22.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹168 (c) ₹144 (d) ₹24
23. 23.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹20 (b) ₹200 (c) ₹180 (d) ₹100
24. 24.If 4 notebooks cost ₹100, how much do 7 notebooks cost? (a) ₹200 (b) ₹175 (c) ₹700 (d) ₹103
25. 25.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹6 (c) ₹12 (d) ₹18
26. 26.If 9 pens cost ₹63, how much do 11 pens cost? (a) ₹77 (b) ₹65 (c) ₹693 (d) ₹84
27. 27.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹84 (d) ₹108
28. 28.If 5 pens cost ₹50, how much do 8 pens cost? (a) ₹80 (b) ₹90 (c) ₹53 (d) ₹400
29. 29.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹165 (c) ₹30 (d) ₹180
30. 30.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
31. 31.₹195 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹195 (b) ₹156 (c) ₹157 (d) ₹39
32. 32.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 11 days (d) 1 day
33. 33.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 13 days (d) 5 days
34. 34.If 3 pens cost ₹30, how much do 2 pens cost? (a) ₹30 (b) ₹60 (c) ₹20 (d) ₹29
35. 35.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 36 days (d) 11 days
36. 36.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹92 (b) ₹46 (c) ₹138 (d) ₹184
37. 37.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 56 days (d) 57 days
38. 38.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 11 days (c) 35 days (d) 17 days
39. 39.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹78 (b) ₹390 (c) ₹39 (d) ₹351
40. 40.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days

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