Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 305 · 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 2 mangoes cost ₹16, how much do 9 mangoes cost? (a) ₹72 (b) ₹23 (c) ₹80 (d) ₹144
2. 2.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹21 (c) ₹7 (d) ₹35
3. 3.If 9 pens cost ₹63, how much do 12 pens cost? (a) ₹66 (b) ₹84 (c) ₹91 (d) ₹756
4. 4.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹78 (b) ₹390 (c) ₹351 (d) ₹39
5. 5.If 5 mangoes cost ₹115, how much do 2 mangoes cost? (a) ₹230 (b) ₹112 (c) ₹69 (d) ₹46
6. 6.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 39 days (c) 40 days (d) 7 days
7. 7.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 6 days (d) 8 days
8. 8.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹110 (d) ₹120
9. 9.4 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) 11 days (d) 7 days
10. 10.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 10 days (d) 11 days
11. 11.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 6 days
12. 12.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹261 (b) ₹290 (c) ₹29 (d) ₹116
13. 13.If 8 mangoes cost ₹160, how much do 10 mangoes cost? (a) ₹220 (b) ₹162 (c) ₹200 (d) ₹1600
14. 14.If 3 notebooks cost ₹54, how much do 10 notebooks cost? (a) ₹198 (b) ₹180 (c) ₹61 (d) ₹540
15. 15.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹35 (d) ₹56
16. 16.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 21 days (d) 13 days
17. 17.₹418 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹342 (d) ₹209
18. 18.If 9 pens cost ₹45, how much do 7 pens cost? (a) ₹43 (b) ₹315 (c) ₹40 (d) ₹35
19. 19.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹13 (b) ₹78 (c) ₹91 (d) ₹65
20. 20.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 1 day
21. 21.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 18 days
22. 22.If 5 mangoes cost ₹15, how much do 10 mangoes cost? (a) ₹20 (b) ₹150 (c) ₹33 (d) ₹30
23. 23.If 7 kites cost ₹21, how much do 10 kites cost? (a) ₹30 (b) ₹24 (c) ₹33 (d) ₹210
24. 24.If 4 mangoes cost ₹72, how much do 8 mangoes cost? (a) ₹162 (b) ₹576 (c) ₹144 (d) ₹76
25. 25.If 6 kites cost ₹108, how much do 3 kites cost? (a) ₹72 (b) ₹324 (c) ₹54 (d) ₹105
26. 26.9 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) 5 days (d) 9 days
27. 27.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹287 (d) ₹246
28. 28.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹80 (b) ₹112 (c) ₹144 (d) ₹16
29. 29.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 9 days (c) 17 days (d) 26 days
30. 30.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 26 days (d) 27 days
31. 31.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹320 (d) ₹260
32. 32.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 14 days (d) 8 days
33. 33.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹30 (c) ₹150 (d) ₹120
34. 34.If 8 notebooks cost ₹184, how much do 4 notebooks cost? (a) ₹736 (b) ₹92 (c) ₹115 (d) ₹180
35. 35.If 9 mangoes cost ₹171, how much do 12 mangoes cost? (a) ₹2052 (b) ₹247 (c) ₹228 (d) ₹174
36. 36.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
37. 37.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹54 (b) ₹144 (c) ₹18 (d) ₹99
38. 38.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹294 (b) ₹231 (c) ₹42 (d) ₹168
39. 39.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹18 (b) ₹33 (c) ₹48 (d) ₹6
40. 40.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 21 days (d) 11 days

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