Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 412 · 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 3 kites cost ₹45, how much do 9 kites cost? (a) ₹405 (b) ₹51 (c) ₹150 (d) ₹135
2. 2.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹216 (b) ₹243 (c) ₹27 (d) ₹217
3. 3.If 7 mangoes cost ₹105, how much do 12 mangoes cost? (a) ₹1260 (b) ₹110 (c) ₹180 (d) ₹195
4. 4.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 9 days
5. 5.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹273 (d) ₹336
6. 6.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 3 days (d) 12 days
7. 7.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹58 (b) ₹59 (c) ₹29 (d) ₹87
8. 8.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 10 days (d) 1 day
9. 9.If 2 pens cost ₹28, how much do 8 pens cost? (a) ₹112 (b) ₹126 (c) ₹224 (d) ₹34
10. 10.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 40 days (d) 7 days
11. 11.If 3 mangoes cost ₹63, how much do 7 mangoes cost? (a) ₹441 (b) ₹67 (c) ₹168 (d) ₹147
12. 12.If 9 kites cost ₹162, how much do 7 kites cost? (a) ₹126 (b) ₹160 (c) ₹144 (d) ₹1134
13. 13.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹78 (b) ₹390 (c) ₹351 (d) ₹39
14. 14.If 4 pens cost ₹16, how much do 5 pens cost? (a) ₹80 (b) ₹20 (c) ₹24 (d) ₹17
15. 15.If 4 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹105 (b) ₹62 (c) ₹90 (d) ₹360
16. 16.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹180 (b) ₹324 (c) ₹252 (d) ₹36
17. 17.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 16 days (d) 17 days
18. 18.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 8 days (d) 14 days
19. 19.₹320 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹200 (b) ₹120 (c) ₹40 (d) ₹160
20. 20.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 16 days
21. 21.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 12 days
22. 22.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹108 (b) ₹81 (c) ₹54 (d) ₹27
23. 23.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 16 days (d) 18 days
24. 24.₹90 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹72 (d) ₹18
25. 25.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹203 (b) ₹232 (c) ₹29 (d) ₹116
26. 26.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹135 (b) ₹225 (c) ₹45 (d) ₹315
27. 27.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹34 (b) ₹102 (c) ₹136 (d) ₹68
28. 28.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 4 days (d) 16 days
29. 29.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹12 (b) ₹10 (c) ₹36 (d) ₹15
30. 30.If 7 pens cost ₹175, how much do 9 pens cost? (a) ₹250 (b) ₹177 (c) ₹225 (d) ₹1575
31. 31.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹100 (b) ₹175 (c) ₹50 (d) ₹250
32. 32.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 11 days
33. 33.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 4 days (d) 6 days
34. 34.₹360 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹360 (b) ₹315 (c) ₹180 (d) ₹45
35. 35.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹46 (b) ₹115 (c) ₹138 (d) ₹23
36. 36.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹387 (b) ₹215 (c) ₹344 (d) ₹43
37. 37.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 8 days
38. 38.6 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) 5 days (d) 7 days
39. 39.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 2 days (d) 8 days
40. 40.If 9 notebooks cost ₹72, how much do 10 notebooks cost? (a) ₹80 (b) ₹720 (c) ₹88 (d) ₹73

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