Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 561 · 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 mangoes cost ₹168, how much do 7 mangoes cost? (a) ₹147 (b) ₹1176 (c) ₹168 (d) ₹167
2. 2.₹352 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹32 (b) ₹176 (c) ₹64 (d) ₹288
3. 3.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹28 (d) ₹21
4. 4.If 6 kites cost ₹30, how much do 2 kites cost? (a) ₹60 (b) ₹10 (c) ₹15 (d) ₹26
5. 5.If 6 kites cost ₹30, how much do 8 kites cost? (a) ₹40 (b) ₹240 (c) ₹32 (d) ₹45
6. 6.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹38 (b) ₹190 (c) ₹342 (d) ₹380
7. 7.If 7 pens cost ₹21, how much do 12 pens cost? (a) ₹39 (b) ₹252 (c) ₹26 (d) ₹36
8. 8.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 5 days (c) 7 days (d) 6 days
9. 9.₹114 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹114 (d) ₹57
10. 10.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 9 days (d) 15 days
11. 11.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹370 (b) ₹333 (c) ₹37 (d) ₹74
12. 12.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹54 (b) ₹6 (c) ₹39 (d) ₹24
13. 13.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹98 (b) ₹84 (c) ₹28 (d) ₹112
14. 14.If 2 kites cost ₹12, how much do 12 kites cost? (a) ₹22 (b) ₹78 (c) ₹144 (d) ₹72
15. 15.If 8 pens cost ₹128, how much do 4 pens cost? (a) ₹124 (b) ₹80 (c) ₹64 (d) ₹512
16. 16.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹22 (c) ₹23 (d) ₹33
17. 17.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 14 days (d) 15 days
18. 18.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹63 (b) ₹43 (c) ₹21 (d) ₹42
19. 19.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹12 (b) ₹72 (c) ₹60 (d) ₹36
20. 20.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 17 days (d) 19 days
21. 21.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹63 (b) ₹126 (c) ₹84 (d) ₹42
22. 22.₹72 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹18 (c) ₹36 (d) ₹54
23. 23.If 2 mangoes cost ₹18, how much do 3 mangoes cost? (a) ₹36 (b) ₹54 (c) ₹27 (d) ₹19
24. 24.If 7 mangoes cost ₹77, how much do 8 mangoes cost? (a) ₹99 (b) ₹78 (c) ₹616 (d) ₹88
25. 25.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 25 days (c) 4 days (d) 5 days
26. 26.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 22 days (d) 21 days
27. 27.If 7 mangoes cost ₹168, how much do 10 mangoes cost? (a) ₹264 (b) ₹240 (c) ₹1680 (d) ₹171
28. 28.If 5 pens cost ₹75, how much do 8 pens cost? (a) ₹120 (b) ₹600 (c) ₹78 (d) ₹135
29. 29.₹150 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹15 (b) ₹135 (c) ₹75 (d) ₹150
30. 30.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹18 (c) ₹6 (d) ₹24
31. 31.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 13 days (d) 22 days
32. 32.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 11 days (d) 2 days
33. 33.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 22 days (d) 21 days
34. 34.If 6 pens cost ₹48, how much do 7 pens cost? (a) ₹49 (b) ₹56 (c) ₹64 (d) ₹336
35. 35.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 24 days (d) 23 days
36. 36.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 14 days (c) 3 days (d) 5 days
37. 37.If 2 pens cost ₹34, how much do 3 pens cost? (a) ₹68 (b) ₹51 (c) ₹35 (d) ₹102
38. 38.If 7 pens cost ₹112, how much do 6 pens cost? (a) ₹111 (b) ₹672 (c) ₹96 (d) ₹112
39. 39.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 17 days (d) 7 days
40. 40.If 3 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹42 (b) ₹126 (c) ₹22 (d) ₹48

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