Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 916 · 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.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹171 (d) ₹19
2. 2.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹114 (d) ₹95
3. 3.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹18 (b) ₹126 (c) ₹72 (d) ₹144
4. 4.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 8 days (d) 10 days
5. 5.If 6 pens cost ₹42, how much do 5 pens cost? (a) ₹41 (b) ₹210 (c) ₹42 (d) ₹35
6. 6.If 4 kites cost ₹80, how much do 7 kites cost? (a) ₹140 (b) ₹560 (c) ₹83 (d) ₹160
7. 7.If 9 mangoes cost ₹135, how much do 5 mangoes cost? (a) ₹131 (b) ₹90 (c) ₹75 (d) ₹675
8. 8.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹49 (b) ₹99 (c) ₹98 (d) ₹147
9. 9.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 5 days
10. 10.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹29 (b) ₹116 (c) ₹145 (d) ₹87
11. 11.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 40 days (c) 20 days (d) 41 days
12. 12.If 8 kites cost ₹48, how much do 9 kites cost? (a) ₹60 (b) ₹49 (c) ₹54 (d) ₹432
13. 13.₹297 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹66 (b) ₹264 (c) ₹33 (d) ₹231
14. 14.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹120 (b) ₹30 (c) ₹15 (d) ₹105
15. 15.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 7 days (d) 16 days
16. 16.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹39 (b) ₹273 (c) ₹312 (d) ₹78
17. 17.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 5 days (d) 6 days
18. 18.If 7 pens cost ₹42, how much do 6 pens cost? (a) ₹41 (b) ₹252 (c) ₹36 (d) ₹42
19. 19.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹56 (d) ₹63
20. 20.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹48 (b) ₹336 (c) ₹168 (d) ₹288
21. 21.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 13 days
22. 22.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹196 (d) ₹168
23. 23.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 12 days (d) 13 days
24. 24.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 14 days
25. 25.If 5 pens cost ₹85, how much do 3 pens cost? (a) ₹83 (b) ₹51 (c) ₹68 (d) ₹255
26. 26.If 2 pens cost ₹14, how much do 10 pens cost? (a) ₹140 (b) ₹22 (c) ₹77 (d) ₹70
27. 27.If 9 pens cost ₹225, how much do 7 pens cost? (a) ₹200 (b) ₹1575 (c) ₹223 (d) ₹175
28. 28.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 12 days (d) 9 days
29. 29.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹116 (b) ₹87 (c) ₹58 (d) ₹29
30. 30.If 4 mangoes cost ₹56, how much do 12 mangoes cost? (a) ₹168 (b) ₹672 (c) ₹64 (d) ₹182
31. 31.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹16 (c) ₹24 (d) ₹20
32. 32.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹110 (d) ₹99
33. 33.If 8 kites cost ₹96, how much do 3 kites cost? (a) ₹91 (b) ₹36 (c) ₹288 (d) ₹48
34. 34.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹34 (b) ₹153 (c) ₹17 (d) ₹170
35. 35.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹46 (b) ₹161 (c) ₹138 (d) ₹184
36. 36.If 3 pens cost ₹18, how much do 4 pens cost? (a) ₹19 (b) ₹24 (c) ₹72 (d) ₹30
37. 37.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹234 (b) ₹195 (c) ₹273 (d) ₹39
38. 38.If 4 mangoes cost ₹92, how much do 7 mangoes cost? (a) ₹184 (b) ₹644 (c) ₹161 (d) ₹95
39. 39.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹224 (b) ₹32 (c) ₹128 (d) ₹256
40. 40.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹60 (b) ₹54 (c) ₹48 (d) ₹12

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