Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 459 · 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.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹6 (c) ₹30 (d) ₹24
2. 2.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹245 (c) ₹35 (d) ₹280
3. 3.₹84 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹28 (b) ₹42 (c) ₹84 (d) ₹56
4. 4.If 4 kites cost ₹20, how much do 2 kites cost? (a) ₹10 (b) ₹15 (c) ₹40 (d) ₹18
5. 5.If 2 notebooks cost ₹48, how much do 6 notebooks cost? (a) ₹144 (b) ₹288 (c) ₹168 (d) ₹52
6. 6.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹150 (c) ₹125 (d) ₹25
7. 7.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 7 days
8. 8.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 22 days (d) 21 days
9. 9.If 9 pens cost ₹27, how much do 5 pens cost? (a) ₹23 (b) ₹135 (c) ₹15 (d) ₹18
10. 10.If 8 notebooks cost ₹80, how much do 3 notebooks cost? (a) ₹240 (b) ₹30 (c) ₹40 (d) ₹75
11. 11.If 6 mangoes cost ₹138, how much do 3 mangoes cost? (a) ₹135 (b) ₹69 (c) ₹92 (d) ₹414
12. 12.If 2 kites cost ₹28, how much do 9 kites cost? (a) ₹140 (b) ₹35 (c) ₹126 (d) ₹252
13. 13.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 12 days (d) 16 days
14. 14.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 9 days
15. 15.If 6 mangoes cost ₹102, how much do 11 mangoes cost? (a) ₹1122 (b) ₹187 (c) ₹107 (d) ₹204
16. 16.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 18 days (d) 3 days
17. 17.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
18. 18.₹30 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹15 (d) ₹30
19. 19.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 13 days (d) 22 days
20. 20.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹148 (b) ₹185 (c) ₹111 (d) ₹37
21. 21.If 6 kites cost ₹54, how much do 2 kites cost? (a) ₹50 (b) ₹108 (c) ₹27 (d) ₹18
22. 22.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 12 days
23. 23.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹128 (b) ₹80 (c) ₹16 (d) ₹104
24. 24.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹40 (d) ₹35
25. 25.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 11 days
26. 26.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹153 (b) ₹17 (c) ₹170 (d) ₹68
27. 27.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹336 (b) ₹144 (c) ₹48 (d) ₹240
28. 28.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹234 (b) ₹195 (c) ₹273 (d) ₹39
29. 29.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 27 days (c) 28 days (d) 26 days
30. 30.If 2 pens cost ₹46, how much do 5 pens cost? (a) ₹115 (b) ₹138 (c) ₹49 (d) ₹230
31. 31.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 7 days (d) 25 days
32. 32.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹43 (b) ₹387 (c) ₹345 (d) ₹344
33. 33.If 5 mangoes cost ₹85, how much do 6 mangoes cost? (a) ₹119 (b) ₹510 (c) ₹102 (d) ₹86
34. 34.If 4 kites cost ₹72, how much do 10 kites cost? (a) ₹78 (b) ₹180 (c) ₹198 (d) ₹720
35. 35.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 8 days (d) 20 days
36. 36.If 2 mangoes cost ₹10, how much do 12 mangoes cost? (a) ₹60 (b) ₹65 (c) ₹120 (d) ₹20
37. 37.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹24 (b) ₹33 (c) ₹6 (d) ₹42
38. 38.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 9 days (d) 1 day
39. 39.If 5 pens cost ₹15, how much do 6 pens cost? (a) ₹16 (b) ₹21 (c) ₹18 (d) ₹90
40. 40.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days

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