Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 697 · 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. 1.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 16 days (d) 4 days
2. 2.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹312 (d) ₹156
3. 3.If 2 kites cost ₹10, how much do 10 kites cost? (a) ₹50 (b) ₹100 (c) ₹18 (d) ₹55
4. 4.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 11 days (d) 9 days
5. 5.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 11 days (d) 12 days
6. 6.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹22 (b) ₹99 (c) ₹198 (d) ₹176
7. 7.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹108 (b) ₹81 (c) ₹27 (d) ₹54
8. 8.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹100 (c) ₹130 (d) ₹20
9. 9.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 2 days (d) 4 days
10. 10.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹78 (b) ₹60 (c) ₹12 (d) ₹96
11. 11.If 6 notebooks cost ₹78, how much do 7 notebooks cost? (a) ₹104 (b) ₹546 (c) ₹91 (d) ₹79
12. 12.If 3 kites cost ₹75, how much do 8 kites cost? (a) ₹80 (b) ₹200 (c) ₹225 (d) ₹600
13. 13.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹91 (b) ₹104 (c) ₹13 (d) ₹52
14. 14.If 3 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹192 (b) ₹64 (c) ₹80 (d) ₹49
15. 15.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹36 (b) ₹24 (c) ₹18 (d) ₹13
16. 16.If 8 mangoes cost ₹136, how much do 6 mangoes cost? (a) ₹134 (b) ₹816 (c) ₹102 (d) ₹119
17. 17.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹325 (b) ₹400 (c) ₹250 (d) ₹50
18. 18.If 2 mangoes cost ₹6, how much do 6 mangoes cost? (a) ₹18 (b) ₹36 (c) ₹10 (d) ₹21
19. 19.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 1 day
20. 20.If 8 notebooks cost ₹120, how much do 2 notebooks cost? (a) ₹114 (b) ₹45 (c) ₹30 (d) ₹240
21. 21.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 1 day (d) 7 days
22. 22.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 6 days (d) 10 days
23. 23.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 39 days (d) 7 days
24. 24.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 6 days (d) 10 days
25. 25.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 18 days
26. 26.If 7 mangoes cost ₹77, how much do 2 mangoes cost? (a) ₹72 (b) ₹33 (c) ₹22 (d) ₹154
27. 27.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹90 (d) ₹81
28. 28.If 5 kites cost ₹20, how much do 7 kites cost? (a) ₹140 (b) ₹22 (c) ₹32 (d) ₹28
29. 29.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 4 days (d) 12 days
30. 30.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹217 (d) ₹248
31. 31.If 2 kites cost ₹48, how much do 5 kites cost? (a) ₹51 (b) ₹120 (c) ₹240 (d) ₹144
32. 32.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹273 (d) ₹234
33. 33.If 6 mangoes cost ₹96, how much do 8 mangoes cost? (a) ₹768 (b) ₹144 (c) ₹98 (d) ₹128
34. 34.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹80 (b) ₹64 (c) ₹16 (d) ₹72
35. 35.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 11 days (d) 7 days
36. 36.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 19 days
37. 37.If 4 pens cost ₹32, how much do 10 pens cost? (a) ₹320 (b) ₹88 (c) ₹38 (d) ₹80
38. 38.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 36 days (c) 35 days (d) 15 days
39. 39.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 12 days
40. 40.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 3 days (d) 2 days

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