Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 629 · 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. 1.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 15 days (d) 5 days
2. 2.If 3 mangoes cost ₹30, how much do 2 mangoes cost? (a) ₹60 (b) ₹20 (c) ₹30 (d) ₹29
3. 3.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 3 days (d) 10 days
4. 4.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹14 (d) ₹15
5. 5.If 4 kites cost ₹20, how much do 9 kites cost? (a) ₹180 (b) ₹50 (c) ₹45 (d) ₹25
6. 6.If 3 mangoes cost ₹75, how much do 10 mangoes cost? (a) ₹82 (b) ₹750 (c) ₹275 (d) ₹250
7. 7.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 8 days (d) 17 days
8. 8.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹300 (b) ₹270 (c) ₹30 (d) ₹150
9. 9.If 5 notebooks cost ₹25, how much do 9 notebooks cost? (a) ₹225 (b) ₹45 (c) ₹29 (d) ₹50
10. 10.₹224 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹64 (d) ₹112
11. 11.If 5 mangoes cost ₹105, how much do 8 mangoes cost? (a) ₹840 (b) ₹108 (c) ₹168 (d) ₹189
12. 12.If 2 pens cost ₹6, how much do 8 pens cost? (a) ₹12 (b) ₹24 (c) ₹27 (d) ₹48
13. 13.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹200 (b) ₹175 (c) ₹25 (d) ₹50
14. 14.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹137 (b) ₹136 (c) ₹17 (d) ₹153
15. 15.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹169 (b) ₹104 (c) ₹26 (d) ₹234
16. 16.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹42 (b) ₹231 (c) ₹126 (d) ₹336
17. 17.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹48 (b) ₹60 (c) ₹30 (d) ₹12
18. 18.If 9 kites cost ₹81, how much do 6 kites cost? (a) ₹78 (b) ₹63 (c) ₹54 (d) ₹486
19. 19.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 21 days (d) 9 days
20. 20.If 7 pens cost ₹49, how much do 8 pens cost? (a) ₹56 (b) ₹50 (c) ₹392 (d) ₹63
21. 21.If 7 mangoes cost ₹21, how much do 6 mangoes cost? (a) ₹126 (b) ₹18 (c) ₹21 (d) ₹20
22. 22.If 3 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹31 (b) ₹120 (c) ₹40 (d) ₹50
23. 23.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹48 (b) ₹6 (c) ₹42 (d) ₹24
24. 24.If 8 notebooks cost ₹64, how much do 4 notebooks cost? (a) ₹256 (b) ₹32 (c) ₹40 (d) ₹60
25. 25.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹84 (d) ₹77
26. 26.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 11 days (d) 27 days
27. 27.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 19 days (c) 12 days (d) 18 days
28. 28.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹231 (b) ₹33 (c) ₹132 (d) ₹264
29. 29.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹243 (c) ₹27 (d) ₹216
30. 30.If 8 pens cost ₹88, how much do 5 pens cost? (a) ₹85 (b) ₹66 (c) ₹55 (d) ₹440
31. 31.If 3 pens cost ₹48, how much do 6 pens cost? (a) ₹112 (b) ₹288 (c) ₹96 (d) ₹51
32. 32.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹6 (b) ₹60 (c) ₹30 (d) ₹54
33. 33.If 6 pens cost ₹36, how much do 4 pens cost? (a) ₹30 (b) ₹24 (c) ₹34 (d) ₹144
34. 34.If 6 kites cost ₹120, how much do 2 kites cost? (a) ₹40 (b) ₹60 (c) ₹116 (d) ₹240
35. 35.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 4 days (d) 27 days
36. 36.If 5 pens cost ₹15, how much do 6 pens cost? (a) ₹16 (b) ₹21 (c) ₹18 (d) ₹90
37. 37.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 6 days (d) 5 days
38. 38.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 11 days (d) 7 days
39. 39.If 5 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹72 (b) ₹118 (c) ₹96 (d) ₹360
40. 40.₹414 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹414 (b) ₹207 (c) ₹46 (d) ₹368

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