Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 469 · 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.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹13 (b) ₹117 (c) ₹52 (d) ₹130
2. 2.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹96 (c) ₹72 (d) ₹24
3. 3.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 16 days (c) 31 days (d) 4 days
4. 4.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 6 days (d) 4 days
5. 5.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹306 (d) ₹340
6. 6.If 5 pens cost ₹100, how much do 9 pens cost? (a) ₹900 (b) ₹104 (c) ₹180 (d) ₹200
7. 7.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
8. 8.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹105 (d) ₹90
9. 9.If 7 pens cost ₹49, how much do 4 pens cost? (a) ₹35 (b) ₹28 (c) ₹46 (d) ₹196
10. 10.If 7 pens cost ₹98, how much do 2 pens cost? (a) ₹28 (b) ₹93 (c) ₹42 (d) ₹196
11. 11.If 3 pens cost ₹18, how much do 4 pens cost? (a) ₹24 (b) ₹19 (c) ₹72 (d) ₹30
12. 12.If 8 mangoes cost ₹144, how much do 3 mangoes cost? (a) ₹139 (b) ₹54 (c) ₹72 (d) ₹432
13. 13.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹175 (b) ₹280 (c) ₹35 (d) ₹315
14. 14.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹120 (b) ₹30 (c) ₹150 (d) ₹135
15. 15.₹180 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹20 (b) ₹140 (c) ₹40 (d) ₹90
16. 16.If 6 kites cost ₹132, how much do 4 kites cost? (a) ₹130 (b) ₹110 (c) ₹88 (d) ₹528
17. 17.If 6 mangoes cost ₹144, how much do 5 mangoes cost? (a) ₹143 (b) ₹120 (c) ₹720 (d) ₹144
18. 18.If 9 mangoes cost ₹126, how much do 4 mangoes cost? (a) ₹121 (b) ₹70 (c) ₹56 (d) ₹504
19. 19.If 7 kites cost ₹126, how much do 4 kites cost? (a) ₹72 (b) ₹90 (c) ₹504 (d) ₹123
20. 20.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 7 days (c) 63 days (d) 64 days
21. 21.If 2 notebooks cost ₹46, how much do 4 notebooks cost? (a) ₹48 (b) ₹184 (c) ₹115 (d) ₹92
22. 22.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 1 day (c) 9 days (d) 3 days
23. 23.If 8 kites cost ₹152, how much do 2 kites cost? (a) ₹304 (b) ₹38 (c) ₹57 (d) ₹146
24. 24.If 9 pens cost ₹144, how much do 3 pens cost? (a) ₹432 (b) ₹138 (c) ₹48 (d) ₹64
25. 25.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 10 days (d) 11 days
26. 26.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
27. 27.If 3 mangoes cost ₹39, how much do 8 mangoes cost? (a) ₹104 (b) ₹117 (c) ₹44 (d) ₹312
28. 28.If 7 kites cost ₹175, how much do 11 kites cost? (a) ₹300 (b) ₹275 (c) ₹1925 (d) ₹179
29. 29.If 5 kites cost ₹40, how much do 4 kites cost? (a) ₹39 (b) ₹40 (c) ₹32 (d) ₹160
30. 30.If 7 pens cost ₹140, how much do 9 pens cost? (a) ₹200 (b) ₹142 (c) ₹180 (d) ₹1260
31. 31.If 3 kites cost ₹72, how much do 9 kites cost? (a) ₹78 (b) ₹216 (c) ₹240 (d) ₹648
32. 32.₹539 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹343 (b) ₹392 (c) ₹49 (d) ₹196
33. 33.If 2 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹23 (b) ₹63 (c) ₹72 (d) ₹126
34. 34.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 20 days (c) 6 days (d) 5 days
35. 35.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹26 (b) ₹234 (c) ₹169 (d) ₹104
36. 36.If 6 pens cost ₹90, how much do 5 pens cost? (a) ₹75 (b) ₹90 (c) ₹450 (d) ₹89
37. 37.If 9 kites cost ₹153, how much do 12 kites cost? (a) ₹156 (b) ₹221 (c) ₹204 (d) ₹1836
38. 38.If 8 pens cost ₹56, how much do 4 pens cost? (a) ₹35 (b) ₹52 (c) ₹28 (d) ₹224
39. 39.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹60 (d) ₹45
40. 40.If 5 kites cost ₹35, how much do 2 kites cost? (a) ₹70 (b) ₹21 (c) ₹32 (d) ₹14

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