Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 170 · 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.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹315 (b) ₹35 (c) ₹175 (d) ₹280
2. 2.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹150 (b) ₹250 (c) ₹50 (d) ₹200
3. 3.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹138 (b) ₹92 (c) ₹69 (d) ₹46
4. 4.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹140 (b) ₹120 (c) ₹40 (d) ₹160
5. 5.₹88 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹66 (b) ₹44 (c) ₹88 (d) ₹22
6. 6.If 3 mangoes cost ₹12, how much do 2 mangoes cost? (a) ₹12 (b) ₹11 (c) ₹24 (d) ₹8
7. 7.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 9 days (d) 16 days
8. 8.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹78 (d) ₹234
9. 9.If 5 notebooks cost ₹115, how much do 6 notebooks cost? (a) ₹161 (b) ₹138 (c) ₹690 (d) ₹116
10. 10.If 2 mangoes cost ₹16, how much do 9 mangoes cost? (a) ₹80 (b) ₹23 (c) ₹144 (d) ₹72
11. 11.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹258 (b) ₹172 (c) ₹43 (d) ₹215
12. 12.If 6 pens cost ₹120, how much do 8 pens cost? (a) ₹160 (b) ₹960 (c) ₹180 (d) ₹122
13. 13.If 8 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹54 (b) ₹60 (c) ₹432 (d) ₹49
14. 14.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
15. 15.If 6 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹35 (b) ₹28 (c) ₹40 (d) ₹168
16. 16.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 11 days (d) 6 days
17. 17.If 5 kites cost ₹35, how much do 6 kites cost? (a) ₹49 (b) ₹210 (c) ₹36 (d) ₹42
18. 18.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 15 days (c) 22 days (d) 7 days
19. 19.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 5 days (d) 20 days
20. 20.If 5 notebooks cost ₹80, how much do 3 notebooks cost? (a) ₹240 (b) ₹64 (c) ₹78 (d) ₹48
21. 21.If 6 mangoes cost ₹138, how much do 12 mangoes cost? (a) ₹144 (b) ₹276 (c) ₹1656 (d) ₹299
22. 22.If 5 pens cost ₹125, how much do 7 pens cost? (a) ₹875 (b) ₹175 (c) ₹200 (d) ₹127
23. 23.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹108 (d) ₹90
24. 24.If 7 mangoes cost ₹105, how much do 4 mangoes cost? (a) ₹75 (b) ₹420 (c) ₹102 (d) ₹60
25. 25.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹56 (c) ₹112 (d) ₹84
26. 26.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹62 (b) ₹186 (c) ₹31 (d) ₹155
27. 27.If 9 notebooks cost ₹27, how much do 5 notebooks cost? (a) ₹15 (b) ₹23 (c) ₹18 (d) ₹135
28. 28.If 9 kites cost ₹207, how much do 2 kites cost? (a) ₹200 (b) ₹46 (c) ₹69 (d) ₹414
29. 29.If 4 kites cost ₹96, how much do 7 kites cost? (a) ₹99 (b) ₹192 (c) ₹168 (d) ₹672
30. 30.If 3 notebooks cost ₹69, how much do 2 notebooks cost? (a) ₹68 (b) ₹69 (c) ₹138 (d) ₹46
31. 31.If 3 notebooks cost ₹75, how much do 4 notebooks cost? (a) ₹300 (b) ₹100 (c) ₹125 (d) ₹76
32. 32.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹15 (c) ₹24 (d) ₹6
33. 33.If 7 kites cost ₹28, how much do 3 kites cost? (a) ₹16 (b) ₹24 (c) ₹84 (d) ₹12
34. 34.If 2 notebooks cost ₹50, how much do 5 notebooks cost? (a) ₹250 (b) ₹150 (c) ₹53 (d) ₹125
35. 35.If 2 pens cost ₹44, how much do 8 pens cost? (a) ₹176 (b) ₹352 (c) ₹50 (d) ₹198
36. 36.If 4 kites cost ₹28, how much do 12 kites cost? (a) ₹36 (b) ₹336 (c) ₹91 (d) ₹84
37. 37.₹451 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹410 (b) ₹41 (c) ₹82 (d) ₹369
38. 38.If 5 kites cost ₹45, how much do 11 kites cost? (a) ₹495 (b) ₹99 (c) ₹108 (d) ₹51
39. 39.If 2 mangoes cost ₹26, how much do 3 mangoes cost? (a) ₹27 (b) ₹78 (c) ₹39 (d) ₹52
40. 40.If 8 kites cost ₹88, how much do 2 kites cost? (a) ₹33 (b) ₹82 (c) ₹176 (d) ₹22

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