Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 347 · 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 7 pens cost ₹91, how much do 4 pens cost? (a) ₹52 (b) ₹65 (c) ₹364 (d) ₹88
2. 2.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹180 (b) ₹45 (c) ₹90 (d) ₹135
3. 3.If 9 pens cost ₹162, how much do 4 pens cost? (a) ₹90 (b) ₹648 (c) ₹157 (d) ₹72
4. 4.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹75 (d) ₹90
5. 5.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹40 (c) ₹25 (d) ₹10
6. 6.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹10 (b) ₹55 (c) ₹80 (d) ₹30
7. 7.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹120 (b) ₹160 (c) ₹40 (d) ₹80
8. 8.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹13 (b) ₹60 (c) ₹15 (d) ₹18
9. 9.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹115 (d) ₹69
10. 10.If 9 mangoes cost ₹99, how much do 3 mangoes cost? (a) ₹33 (b) ₹93 (c) ₹44 (d) ₹297
11. 11.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹72 (d) ₹36
12. 12.If 5 mangoes cost ₹70, how much do 4 mangoes cost? (a) ₹280 (b) ₹70 (c) ₹69 (d) ₹56
13. 13.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹108 (b) ₹24 (c) ₹66 (d) ₹12
14. 14.If 9 kites cost ₹198, how much do 10 kites cost? (a) ₹199 (b) ₹220 (c) ₹1980 (d) ₹242
15. 15.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 11 days (d) 9 days
16. 16.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹33 (b) ₹198 (c) ₹199 (d) ₹231
17. 17.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹78 (b) ₹117 (c) ₹156 (d) ₹39
18. 18.If 3 notebooks cost ₹30, how much do 11 notebooks cost? (a) ₹120 (b) ₹330 (c) ₹110 (d) ₹38
19. 19.If 6 pens cost ₹48, how much do 12 pens cost? (a) ₹96 (b) ₹576 (c) ₹104 (d) ₹54
20. 20.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
21. 21.If 9 pens cost ₹27, how much do 10 pens cost? (a) ₹270 (b) ₹28 (c) ₹30 (d) ₹33
22. 22.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹41 (b) ₹328 (c) ₹205 (d) ₹369
23. 23.If 9 kites cost ₹117, how much do 12 kites cost? (a) ₹1404 (b) ₹120 (c) ₹156 (d) ₹169
24. 24.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 19 days (d) 7 days
25. 25.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 17 days (c) 11 days (d) 36 days
26. 26.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 5 days (d) 3 days
27. 27.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 11 days (d) 1 day
28. 28.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 21 days (c) 7 days (d) 63 days
29. 29.₹423 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹47 (b) ₹376 (c) ₹423 (d) ₹377
30. 30.If 6 kites cost ₹48, how much do 10 kites cost? (a) ₹88 (b) ₹52 (c) ₹480 (d) ₹80
31. 31.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹170 (d) ₹153
32. 32.If 2 mangoes cost ₹14, how much do 3 mangoes cost? (a) ₹42 (b) ₹21 (c) ₹28 (d) ₹15
33. 33.If 9 kites cost ₹45, how much do 3 kites cost? (a) ₹135 (b) ₹39 (c) ₹20 (d) ₹15
34. 34.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹5 (b) ₹15 (c) ₹20 (d) ₹10
35. 35.If 2 kites cost ₹24, how much do 11 kites cost? (a) ₹144 (b) ₹132 (c) ₹264 (d) ₹33
36. 36.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 6 days (d) 5 days
37. 37.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹25 (b) ₹10 (c) ₹30 (d) ₹20
38. 38.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 6 days (d) 5 days
39. 39.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹104 (b) ₹78 (c) ₹26 (d) ₹91
40. 40.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹60 (d) ₹12

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