Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 354 · 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.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹224 (d) ₹144
2. 2.If 8 kites cost ₹64, how much do 9 kites cost? (a) ₹65 (b) ₹576 (c) ₹80 (d) ₹72
3. 3.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹138 (d) ₹115
4. 4.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹25 (d) ₹30
5. 5.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹225 (b) ₹250 (c) ₹50 (d) ₹25
6. 6.If 2 notebooks cost ₹22, how much do 8 notebooks cost? (a) ₹99 (b) ₹28 (c) ₹176 (d) ₹88
7. 7.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹50 (d) ₹60
8. 8.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹260 (b) ₹200 (c) ₹320 (d) ₹40
9. 9.If 7 notebooks cost ₹77, how much do 4 notebooks cost? (a) ₹55 (b) ₹308 (c) ₹44 (d) ₹74
10. 10.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹8 (c) ₹24 (d) ₹16
11. 11.If 5 pens cost ₹40, how much do 7 pens cost? (a) ₹42 (b) ₹280 (c) ₹56 (d) ₹64
12. 12.If 9 kites cost ₹189, how much do 7 kites cost? (a) ₹168 (b) ₹1323 (c) ₹187 (d) ₹147
13. 13.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 15 days (d) 7 days
14. 14.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹60 (b) ₹135 (c) ₹150 (d) ₹15
15. 15.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 41 days (b) 40 days (c) 4 days (d) 16 days
16. 16.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
17. 17.If 2 pens cost ₹36, how much do 3 pens cost? (a) ₹108 (b) ₹37 (c) ₹54 (d) ₹72
18. 18.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹116 (b) ₹232 (c) ₹29 (d) ₹203
19. 19.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 7 days (d) 2 days
20. 20.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹304 (b) ₹114 (c) ₹209 (d) ₹38
21. 21.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹46 (c) ₹138 (d) ₹92
22. 22.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹90 (b) ₹150 (c) ₹30 (d) ₹180
23. 23.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 10 days (d) 11 days
24. 24.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹123 (b) ₹205 (c) ₹164 (d) ₹41
25. 25.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 18 days (c) 19 days (d) 11 days
26. 26.₹231 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹198 (b) ₹66 (c) ₹33 (d) ₹165
27. 27.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 11 days (d) 10 days
28. 28.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹63 (c) ₹7 (d) ₹56
29. 29.If 3 pens cost ₹72, how much do 4 pens cost? (a) ₹73 (b) ₹120 (c) ₹96 (d) ₹288
30. 30.If 5 kites cost ₹65, how much do 9 kites cost? (a) ₹130 (b) ₹69 (c) ₹117 (d) ₹585
31. 31.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 6 days (d) 7 days
32. 32.If 6 mangoes cost ₹138, how much do 4 mangoes cost? (a) ₹115 (b) ₹136 (c) ₹552 (d) ₹92
33. 33.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 27 days (d) 28 days
34. 34.If 6 pens cost ₹102, how much do 10 pens cost? (a) ₹170 (b) ₹1020 (c) ₹187 (d) ₹106
35. 35.5 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
36. 36.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 17 days (d) 4 days
37. 37.If 7 kites cost ₹154, how much do 3 kites cost? (a) ₹88 (b) ₹150 (c) ₹66 (d) ₹462
38. 38.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹297 (b) ₹165 (c) ₹33 (d) ₹231
39. 39.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹246 (c) ₹41 (d) ₹287
40. 40.If 3 notebooks cost ₹45, how much do 12 notebooks cost? (a) ₹180 (b) ₹195 (c) ₹54 (d) ₹540

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