Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 932 · 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.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹24 (b) ₹84 (c) ₹54 (d) ₹12
2. 2.If 2 kites cost ₹24, how much do 10 kites cost? (a) ₹240 (b) ₹32 (c) ₹132 (d) ₹120
3. 3.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 4 days
4. 4.If 9 kites cost ₹126, how much do 2 kites cost? (a) ₹28 (b) ₹119 (c) ₹42 (d) ₹252
5. 5.₹270 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹270 (b) ₹135 (c) ₹243 (d) ₹27
6. 6.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 2 days (d) 14 days
7. 7.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 8 days (d) 2 days
8. 8.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹192 (b) ₹32 (c) ₹112 (d) ₹224
9. 9.If 6 kites cost ₹48, how much do 7 kites cost? (a) ₹49 (b) ₹64 (c) ₹56 (d) ₹336
10. 10.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 4 days (d) 19 days
11. 11.If 8 kites cost ₹152, how much do 4 kites cost? (a) ₹76 (b) ₹608 (c) ₹148 (d) ₹95
12. 12.If 6 mangoes cost ₹66, how much do 3 mangoes cost? (a) ₹198 (b) ₹33 (c) ₹63 (d) ₹44
13. 13.If 8 notebooks cost ₹160, how much do 9 notebooks cost? (a) ₹200 (b) ₹1440 (c) ₹161 (d) ₹180
14. 14.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 7 days (d) 9 days
15. 15.If 9 kites cost ₹27, how much do 7 kites cost? (a) ₹25 (b) ₹24 (c) ₹189 (d) ₹21
16. 16.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹100 (c) ₹10 (d) ₹50
17. 17.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 5 days (d) 13 days
18. 18.If 8 notebooks cost ₹136, how much do 4 notebooks cost? (a) ₹85 (b) ₹132 (c) ₹544 (d) ₹68
19. 19.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹400 (b) ₹50 (c) ₹350 (d) ₹200
20. 20.If 2 notebooks cost ₹20, how much do 10 notebooks cost? (a) ₹100 (b) ₹28 (c) ₹200 (d) ₹110
21. 21.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
22. 22.₹432 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹432 (b) ₹48 (c) ₹216 (d) ₹384
23. 23.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 10 days (d) 2 days
24. 24.₹195 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹195 (d) ₹157
25. 25.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 13 days (c) 16 days (d) 1 day
26. 26.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 16 days (d) 9 days
27. 27.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹216 (b) ₹96 (c) ₹24 (d) ₹156
28. 28.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹48 (b) ₹39 (c) ₹30 (d) ₹6
29. 29.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 11 days
30. 30.If 9 notebooks cost ₹54, how much do 11 notebooks cost? (a) ₹594 (b) ₹56 (c) ₹72 (d) ₹66
31. 31.If 3 pens cost ₹21, how much do 6 pens cost? (a) ₹42 (b) ₹49 (c) ₹126 (d) ₹24
32. 32.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 17 days (d) 10 days
33. 33.If 8 kites cost ₹24, how much do 6 kites cost? (a) ₹18 (b) ₹144 (c) ₹21 (d) ₹22
34. 34.If 9 mangoes cost ₹216, how much do 2 mangoes cost? (a) ₹72 (b) ₹48 (c) ₹432 (d) ₹209
35. 35.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 26 days (c) 16 days (d) 27 days
36. 36.₹224 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹224 (d) ₹112
37. 37.If 2 notebooks cost ₹8, how much do 10 notebooks cost? (a) ₹16 (b) ₹80 (c) ₹40 (d) ₹44
38. 38.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 28 days (d) 16 days
39. 39.If 2 kites cost ₹26, how much do 3 kites cost? (a) ₹27 (b) ₹52 (c) ₹39 (d) ₹78
40. 40.If 2 mangoes cost ₹34, how much do 11 mangoes cost? (a) ₹374 (b) ₹43 (c) ₹187 (d) ₹204

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