Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 914 · 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.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹30 (c) ₹150 (d) ₹240
2. 2.If 3 pens cost ₹12, how much do 7 pens cost? (a) ₹84 (b) ₹32 (c) ₹16 (d) ₹28
3. 3.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹72 (b) ₹144 (c) ₹24 (d) ₹120
4. 4.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹38 (b) ₹57 (c) ₹19 (d) ₹39
5. 5.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹120 (c) ₹40 (d) ₹80
6. 6.If 6 notebooks cost ₹132, how much do 7 notebooks cost? (a) ₹924 (b) ₹176 (c) ₹133 (d) ₹154
7. 7.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
8. 8.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 8 days (d) 9 days
9. 9.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹160 (b) ₹192 (c) ₹32 (d) ₹224
10. 10.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹13 (b) ₹130 (c) ₹117 (d) ₹52
11. 11.If 5 mangoes cost ₹25, how much do 6 mangoes cost? (a) ₹30 (b) ₹150 (c) ₹35 (d) ₹26
12. 12.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 27 days (c) 15 days (d) 3 days
13. 13.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 6 days (d) 4 days
14. 14.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 2 days (d) 8 days
15. 15.If 6 mangoes cost ₹66, how much do 11 mangoes cost? (a) ₹132 (b) ₹726 (c) ₹71 (d) ₹121
16. 16.If 9 mangoes cost ₹45, how much do 5 mangoes cost? (a) ₹30 (b) ₹41 (c) ₹25 (d) ₹225
17. 17.If 2 kites cost ₹28, how much do 5 kites cost? (a) ₹140 (b) ₹31 (c) ₹84 (d) ₹70
18. 18.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹182 (d) ₹156
19. 19.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 14 days (d) 20 days
20. 20.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 11 days (d) 1 day
21. 21.₹96 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹96 (b) ₹84 (c) ₹48 (d) ₹12
22. 22.If 2 pens cost ₹26, how much do 11 pens cost? (a) ₹35 (b) ₹286 (c) ₹143 (d) ₹156
23. 23.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 13 days (c) 30 days (d) 17 days
24. 24.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹312 (b) ₹273 (c) ₹156 (d) ₹39
25. 25.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹36 (d) ₹30
26. 26.If 6 kites cost ₹84, how much do 3 kites cost? (a) ₹252 (b) ₹81 (c) ₹42 (d) ₹56
27. 27.If 8 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹144 (b) ₹43 (c) ₹18 (d) ₹24
28. 28.If 7 mangoes cost ₹147, how much do 12 mangoes cost? (a) ₹273 (b) ₹252 (c) ₹1764 (d) ₹152
29. 29.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 16 days (d) 14 days
30. 30.If 2 pens cost ₹46, how much do 3 pens cost? (a) ₹92 (b) ₹138 (c) ₹69 (d) ₹47
31. 31.If 8 pens cost ₹24, how much do 4 pens cost? (a) ₹15 (b) ₹12 (c) ₹96 (d) ₹20
32. 32.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 18 days (d) 19 days
33. 33.If 7 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹26 (b) ₹20 (c) ₹140 (d) ₹24
34. 34.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹20 (d) ₹40
35. 35.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹216 (d) ₹156
36. 36.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹198 (d) ₹165
37. 37.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
38. 38.If 2 pens cost ₹12, how much do 9 pens cost? (a) ₹60 (b) ₹54 (c) ₹108 (d) ₹19
39. 39.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 16 days (c) 26 days (d) 10 days
40. 40.If 9 mangoes cost ₹162, how much do 10 mangoes cost? (a) ₹198 (b) ₹180 (c) ₹1620 (d) ₹163

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