Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 76 · 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.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹322 (b) ₹46 (c) ₹230 (d) ₹414
2. 2.If 4 notebooks cost ₹20, how much do 2 notebooks cost? (a) ₹10 (b) ₹40 (c) ₹18 (d) ₹15
3. 3.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹38 (b) ₹209 (c) ₹266 (d) ₹152
4. 4.If 9 mangoes cost ₹180, how much do 3 mangoes cost? (a) ₹540 (b) ₹80 (c) ₹174 (d) ₹60
5. 5.If 3 pens cost ₹69, how much do 12 pens cost? (a) ₹78 (b) ₹276 (c) ₹299 (d) ₹828
6. 6.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹90 (b) ₹30 (c) ₹120 (d) ₹105
7. 7.If 6 mangoes cost ₹48, how much do 5 mangoes cost? (a) ₹240 (b) ₹47 (c) ₹40 (d) ₹48
8. 8.If 3 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹96 (b) ₹288 (c) ₹120 (d) ₹73
9. 9.₹143 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹130 (b) ₹117 (c) ₹26 (d) ₹13
10. 10.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 15 days (c) 5 days (d) 6 days
11. 11.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹180 (d) ₹165
12. 12.If 7 pens cost ₹49, how much do 4 pens cost? (a) ₹35 (b) ₹46 (c) ₹28 (d) ₹196
13. 13.If 9 kites cost ₹216, how much do 3 kites cost? (a) ₹648 (b) ₹72 (c) ₹96 (d) ₹210
14. 14.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹44 (d) ₹88
15. 15.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 14 days (c) 24 days (d) 2 days
16. 16.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 8 days
17. 17.If 8 notebooks cost ₹96, how much do 12 notebooks cost? (a) ₹156 (b) ₹144 (c) ₹100 (d) ₹1152
18. 18.If 4 notebooks cost ₹96, how much do 5 notebooks cost? (a) ₹480 (b) ₹120 (c) ₹97 (d) ₹144
19. 19.If 4 pens cost ₹12, how much do 12 pens cost? (a) ₹20 (b) ₹39 (c) ₹36 (d) ₹144
20. 20.If 8 kites cost ₹56, how much do 4 kites cost? (a) ₹35 (b) ₹52 (c) ₹224 (d) ₹28
21. 21.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 36 days (d) 4 days
22. 22.If 8 kites cost ₹64, how much do 2 kites cost? (a) ₹24 (b) ₹128 (c) ₹16 (d) ₹58
23. 23.If 2 kites cost ₹36, how much do 3 kites cost? (a) ₹108 (b) ₹72 (c) ₹54 (d) ₹37
24. 24.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 8 days (d) 7 days
25. 25.₹152 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹57 (b) ₹19 (c) ₹76 (d) ₹95
26. 26.₹231 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹165 (b) ₹66 (c) ₹198 (d) ₹33
27. 27.If 9 pens cost ₹81, how much do 7 pens cost? (a) ₹567 (b) ₹72 (c) ₹79 (d) ₹63
28. 28.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹56 (d) ₹49
29. 29.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹8 (b) ₹32 (c) ₹24 (d) ₹40
30. 30.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹18 (b) ₹180 (c) ₹162 (d) ₹90
31. 31.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹24 (c) ₹16 (d) ₹8
32. 32.If 3 notebooks cost ₹39, how much do 11 notebooks cost? (a) ₹47 (b) ₹429 (c) ₹143 (d) ₹156
33. 33.₹66 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹66 (b) ₹44 (c) ₹33 (d) ₹22
34. 34.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹200 (b) ₹280 (c) ₹120 (d) ₹40
35. 35.If 4 pens cost ₹32, how much do 8 pens cost? (a) ₹72 (b) ₹256 (c) ₹36 (d) ₹64
36. 36.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 48 days (b) 3 days (c) 4 days (d) 21 days
37. 37.If 2 mangoes cost ₹6, how much do 4 mangoes cost? (a) ₹8 (b) ₹12 (c) ₹24 (d) ₹15
38. 38.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹24 (b) ₹120 (c) ₹132 (d) ₹144
39. 39.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹111 (d) ₹74
40. 40.9 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) 19 days (d) 18 days

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