Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 357 · 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.If 4 kites cost ₹96, how much do 6 kites cost? (a) ₹168 (b) ₹98 (c) ₹144 (d) ₹576
2. 2.If 3 notebooks cost ₹69, how much do 6 notebooks cost? (a) ₹414 (b) ₹138 (c) ₹161 (d) ₹72
3. 3.If 3 pens cost ₹60, how much do 6 pens cost? (a) ₹360 (b) ₹140 (c) ₹63 (d) ₹120
4. 4.If 6 mangoes cost ₹138, how much do 4 mangoes cost? (a) ₹92 (b) ₹136 (c) ₹552 (d) ₹115
5. 5.If 6 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹40 (b) ₹31 (c) ₹210 (d) ₹35
6. 6.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹200 (b) ₹280 (c) ₹240 (d) ₹40
7. 7.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹315 (d) ₹175
8. 8.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹99 (d) ₹132
9. 9.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 23 days (d) 12 days
10. 10.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹68 (d) ₹85
11. 11.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹60 (b) ₹120 (c) ₹12 (d) ₹108
12. 12.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 6 days (d) 8 days
13. 13.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹343 (b) ₹245 (c) ₹441 (d) ₹49
14. 14.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹55 (b) ₹66 (c) ₹11 (d) ₹77
15. 15.If 6 pens cost ₹54, how much do 8 pens cost? (a) ₹56 (b) ₹81 (c) ₹72 (d) ₹432
16. 16.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 15 days (d) 13 days
17. 17.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 9 days (d) 26 days
18. 18.If 5 mangoes cost ₹25, how much do 6 mangoes cost? (a) ₹35 (b) ₹150 (c) ₹26 (d) ₹30
19. 19.If 7 notebooks cost ₹77, how much do 10 notebooks cost? (a) ₹80 (b) ₹110 (c) ₹770 (d) ₹121
20. 20.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 13 days (d) 16 days
21. 21.If 4 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹64 (b) ₹56 (c) ₹224 (d) ₹35
22. 22.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 19 days (d) 14 days
23. 23.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
24. 24.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 7 days (d) 5 days
25. 25.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹136 (b) ₹170 (c) ₹34 (d) ₹153
26. 26.₹150 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹75 (b) ₹150 (c) ₹135 (d) ₹15
27. 27.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 3 days (d) 12 days
28. 28.If 6 mangoes cost ₹114, how much do 9 mangoes cost? (a) ₹117 (b) ₹1026 (c) ₹190 (d) ₹171
29. 29.If 5 kites cost ₹70, how much do 3 kites cost? (a) ₹56 (b) ₹68 (c) ₹42 (d) ₹210
30. 30.If 3 pens cost ₹54, how much do 6 pens cost? (a) ₹126 (b) ₹324 (c) ₹108 (d) ₹57
31. 31.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
32. 32.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 10 days (d) 16 days
33. 33.If 9 mangoes cost ₹189, how much do 10 mangoes cost? (a) ₹210 (b) ₹190 (c) ₹1890 (d) ₹231
34. 34.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹160 (b) ₹128 (c) ₹96 (d) ₹32
35. 35.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹147 (b) ₹105 (c) ₹126 (d) ₹21
36. 36.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
37. 37.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 12 days (d) 10 days
38. 38.If 4 mangoes cost ₹100, how much do 3 mangoes cost? (a) ₹100 (b) ₹75 (c) ₹99 (d) ₹300
39. 39.If 2 kites cost ₹20, how much do 7 kites cost? (a) ₹80 (b) ₹25 (c) ₹70 (d) ₹140
40. 40.₹441 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹343 (b) ₹49 (c) ₹98 (d) ₹392

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