Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 803 · 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.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹75 (b) ₹100 (c) ₹25 (d) ₹50
2. 2.If 9 notebooks cost ₹72, how much do 2 notebooks cost? (a) ₹65 (b) ₹144 (c) ₹16 (d) ₹24
3. 3.If 5 kites cost ₹80, how much do 6 kites cost? (a) ₹96 (b) ₹480 (c) ₹112 (d) ₹81
4. 4.If 2 pens cost ₹24, how much do 10 pens cost? (a) ₹132 (b) ₹120 (c) ₹32 (d) ₹240
5. 5.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 13 days (d) 1 day
6. 6.If 5 notebooks cost ₹85, how much do 2 notebooks cost? (a) ₹170 (b) ₹34 (c) ₹51 (d) ₹82
7. 7.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 10 days (d) 14 days
8. 8.If 3 pens cost ₹72, how much do 12 pens cost? (a) ₹312 (b) ₹288 (c) ₹864 (d) ₹81
9. 9.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹99 (b) ₹49 (c) ₹147 (d) ₹98
10. 10.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹230 (d) ₹207
11. 11.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹44 (b) ₹396 (c) ₹308 (d) ₹220
12. 12.If 2 notebooks cost ₹38, how much do 10 notebooks cost? (a) ₹380 (b) ₹209 (c) ₹46 (d) ₹190
13. 13.If 2 mangoes cost ₹12, how much do 6 mangoes cost? (a) ₹42 (b) ₹16 (c) ₹36 (d) ₹72
14. 14.If 2 kites cost ₹42, how much do 5 kites cost? (a) ₹105 (b) ₹45 (c) ₹210 (d) ₹126
15. 15.If 9 pens cost ₹171, how much do 6 pens cost? (a) ₹133 (b) ₹114 (c) ₹168 (d) ₹1026
16. 16.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹441 (b) ₹490 (c) ₹49 (d) ₹98
17. 17.If 2 notebooks cost ₹44, how much do 8 notebooks cost? (a) ₹198 (b) ₹176 (c) ₹352 (d) ₹50
18. 18.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 43 days (c) 42 days (d) 7 days
19. 19.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 4 days
20. 20.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 11 days
21. 21.3 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
22. 22.₹272 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹102 (b) ₹170 (c) ₹136 (d) ₹34
23. 23.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹121 (b) ₹132 (c) ₹110 (d) ₹22
24. 24.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 3 days
25. 25.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 20 days (c) 5 days (d) 36 days
26. 26.If 4 mangoes cost ₹84, how much do 9 mangoes cost? (a) ₹89 (b) ₹756 (c) ₹210 (d) ₹189
27. 27.If 6 kites cost ₹102, how much do 4 kites cost? (a) ₹408 (b) ₹85 (c) ₹68 (d) ₹100
28. 28.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 7 days (d) 9 days
29. 29.If 7 mangoes cost ₹140, how much do 12 mangoes cost? (a) ₹240 (b) ₹145 (c) ₹260 (d) ₹1680
30. 30.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹70 (d) ₹14
31. 31.If 6 pens cost ₹36, how much do 11 pens cost? (a) ₹41 (b) ₹396 (c) ₹66 (d) ₹72
32. 32.If 4 notebooks cost ₹76, how much do 12 notebooks cost? (a) ₹228 (b) ₹84 (c) ₹247 (d) ₹912
33. 33.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 13 days (d) 12 days
34. 34.If 2 kites cost ₹36, how much do 5 kites cost? (a) ₹108 (b) ₹90 (c) ₹39 (d) ₹180
35. 35.If 8 kites cost ₹192, how much do 5 kites cost? (a) ₹144 (b) ₹120 (c) ₹189 (d) ₹960
36. 36.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 19 days
37. 37.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 17 days (c) 5 days (d) 34 days
38. 38.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 15 days
39. 39.If 4 pens cost ₹20, how much do 11 pens cost? (a) ₹60 (b) ₹27 (c) ₹220 (d) ₹55
40. 40.If 2 mangoes cost ₹14, how much do 4 mangoes cost? (a) ₹16 (b) ₹56 (c) ₹35 (d) ₹28

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