Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 177 · 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 kites cost ₹88, how much do 12 kites cost? (a) ₹143 (b) ₹1056 (c) ₹132 (d) ₹92
2. 2.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹115 (b) ₹93 (c) ₹23 (d) ₹92
3. 3.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹35 (d) ₹28
4. 4.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 14 days (b) 7 days (c) 6 days (d) 5 days
5. 5.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹17 (b) ₹51 (c) ₹85 (d) ₹68
6. 6.If 8 mangoes cost ₹152, how much do 6 mangoes cost? (a) ₹912 (b) ₹133 (c) ₹114 (d) ₹150
7. 7.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 17 days (d) 9 days
8. 8.If 4 pens cost ₹52, how much do 6 pens cost? (a) ₹54 (b) ₹91 (c) ₹312 (d) ₹78
9. 9.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹360 (d) ₹280
10. 10.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 5 days
11. 11.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 5 days (d) 4 days
12. 12.If 6 notebooks cost ₹102, how much do 3 notebooks cost? (a) ₹306 (b) ₹51 (c) ₹99 (d) ₹68
13. 13.If 7 pens cost ₹63, how much do 9 pens cost? (a) ₹90 (b) ₹81 (c) ₹567 (d) ₹65
14. 14.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹175 (b) ₹200 (c) ₹150 (d) ₹50
15. 15.If 3 mangoes cost ₹63, how much do 9 mangoes cost? (a) ₹210 (b) ₹189 (c) ₹69 (d) ₹567
16. 16.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 2 days
17. 17.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 18 days (d) 2 days
18. 18.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹273 (b) ₹336 (c) ₹210 (d) ₹42
19. 19.If 2 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹180 (b) ₹44 (c) ₹360 (d) ₹198
20. 20.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹33 (b) ₹77 (c) ₹55 (d) ₹11
21. 21.9 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
22. 22.If 7 kites cost ₹21, how much do 11 kites cost? (a) ₹25 (b) ₹36 (c) ₹33 (d) ₹231
23. 23.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 16 days (d) 4 days
24. 24.₹500 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹150 (b) ₹250 (c) ₹350 (d) ₹50
25. 25.If 3 pens cost ₹21, how much do 5 pens cost? (a) ₹23 (b) ₹105 (c) ₹42 (d) ₹35
26. 26.If 6 kites cost ₹90, how much do 7 kites cost? (a) ₹91 (b) ₹630 (c) ₹120 (d) ₹105
27. 27.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹69 (c) ₹138 (d) ₹92
28. 28.If 7 kites cost ₹126, how much do 8 kites cost? (a) ₹127 (b) ₹162 (c) ₹144 (d) ₹1008
29. 29.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
30. 30.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹60 (b) ₹135 (c) ₹150 (d) ₹15
31. 31.If 5 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹96 (b) ₹420 (c) ₹84 (d) ₹62
32. 32.If 8 pens cost ₹40, how much do 4 pens cost? (a) ₹25 (b) ₹36 (c) ₹160 (d) ₹20
33. 33.If 6 kites cost ₹54, how much do 8 kites cost? (a) ₹432 (b) ₹56 (c) ₹81 (d) ₹72
34. 34.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 13 days (d) 5 days
35. 35.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 8 days
36. 36.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹152 (b) ₹19 (c) ₹57 (d) ₹171
37. 37.If 4 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹30 (b) ₹27 (c) ₹108 (d) ₹17
38. 38.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹92 (b) ₹207 (c) ₹23 (d) ₹230
39. 39.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 12 days (d) 7 days
40. 40.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹58 (b) ₹116 (c) ₹87 (d) ₹29

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