Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 249 · 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 5 pens cost ₹95, how much do 6 pens cost? (a) ₹133 (b) ₹96 (c) ₹114 (d) ₹570
2. 2.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹14 (b) ₹28 (c) ₹77 (d) ₹126
3. 3.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹224 (b) ₹28 (c) ₹140 (d) ₹182
4. 4.If 4 pens cost ₹60, how much do 5 pens cost? (a) ₹61 (b) ₹90 (c) ₹300 (d) ₹75
5. 5.₹250 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹200 (c) ₹125 (d) ₹250
6. 6.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 7 days
7. 7.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹414 (d) ₹322
8. 8.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 17 days (c) 3 days (d) 32 days
9. 9.If 9 notebooks cost ₹144, how much do 7 notebooks cost? (a) ₹128 (b) ₹142 (c) ₹112 (d) ₹1008
10. 10.If 8 mangoes cost ₹184, how much do 9 mangoes cost? (a) ₹207 (b) ₹230 (c) ₹185 (d) ₹1656
11. 11.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹47 (b) ₹423 (c) ₹329 (d) ₹235
12. 12.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 43 days (c) 42 days (d) 7 days
13. 13.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 16 days (d) 2 days
14. 14.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 23 days (d) 22 days
15. 15.If 8 kites cost ₹96, how much do 2 kites cost? (a) ₹90 (b) ₹36 (c) ₹192 (d) ₹24
16. 16.If 2 pens cost ₹12, how much do 12 pens cost? (a) ₹72 (b) ₹78 (c) ₹144 (d) ₹22
17. 17.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 14 days (d) 8 days
18. 18.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 13 days (d) 21 days
19. 19.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹171 (b) ₹38 (c) ₹76 (d) ₹266
20. 20.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 2 days
21. 21.If 6 notebooks cost ₹144, how much do 8 notebooks cost? (a) ₹1152 (b) ₹146 (c) ₹216 (d) ₹192
22. 22.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹42 (d) ₹35
23. 23.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹24 (c) ₹40 (d) ₹8
24. 24.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 9 days (d) 49 days
25. 25.If 5 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹84 (b) ₹72 (c) ₹61 (d) ₹360
26. 26.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
27. 27.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 14 days (d) 15 days
28. 28.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 7 days (d) 5 days
29. 29.If 3 kites cost ₹75, how much do 4 kites cost? (a) ₹76 (b) ₹300 (c) ₹100 (d) ₹125
30. 30.₹224 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹28 (b) ₹224 (c) ₹196 (d) ₹112
31. 31.If 3 pens cost ₹54, how much do 2 pens cost? (a) ₹53 (b) ₹108 (c) ₹54 (d) ₹36
32. 32.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹165 (b) ₹33 (c) ₹231 (d) ₹198
33. 33.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹68 (b) ₹34 (c) ₹102 (d) ₹136
34. 34.If 3 pens cost ₹30, how much do 5 pens cost? (a) ₹32 (b) ₹50 (c) ₹60 (d) ₹150
35. 35.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹300 (b) ₹250 (c) ₹275 (d) ₹50
36. 36.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹133 (d) ₹152
37. 37.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 17 days (d) 39 days
38. 38.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
39. 39.If 9 kites cost ₹27, how much do 3 kites cost? (a) ₹9 (b) ₹21 (c) ₹12 (d) ₹81
40. 40.If 3 notebooks cost ₹72, how much do 11 notebooks cost? (a) ₹792 (b) ₹288 (c) ₹264 (d) ₹80

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