Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 175 · 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. 1.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 10 days (d) 18 days
2. 2.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹85 (b) ₹102 (c) ₹17 (d) ₹119
3. 3.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹63 (c) ₹84 (d) ₹126
4. 4.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹13 (b) ₹104 (c) ₹39 (d) ₹117
5. 5.If 3 kites cost ₹72, how much do 12 kites cost? (a) ₹288 (b) ₹81 (c) ₹312 (d) ₹864
6. 6.If 8 kites cost ₹152, how much do 2 kites cost? (a) ₹38 (b) ₹146 (c) ₹57 (d) ₹304
7. 7.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 29 days (d) 28 days
8. 8.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 1 day
9. 9.₹180 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹80 (b) ₹100 (c) ₹90 (d) ₹20
10. 10.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 1 day (d) 11 days
11. 11.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹38 (b) ₹144 (c) ₹90 (d) ₹72
12. 12.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 14 days (d) 3 days
13. 13.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹196 (b) ₹245 (c) ₹49 (d) ₹294
14. 14.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 3 days (d) 2 days
15. 15.If 3 pens cost ₹51, how much do 10 pens cost? (a) ₹187 (b) ₹510 (c) ₹58 (d) ₹170
16. 16.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹7 (b) ₹12 (c) ₹18 (d) ₹9
17. 17.If 9 mangoes cost ₹108, how much do 3 mangoes cost? (a) ₹102 (b) ₹36 (c) ₹48 (d) ₹324
18. 18.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 2 days (c) 3 days (d) 32 days
19. 19.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹5 (b) ₹50 (c) ₹45 (d) ₹20
20. 20.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 16 days (d) 13 days
21. 21.If 2 mangoes cost ₹14, how much do 11 mangoes cost? (a) ₹154 (b) ₹84 (c) ₹77 (d) ₹23
22. 22.If 4 notebooks cost ₹68, how much do 12 notebooks cost? (a) ₹76 (b) ₹816 (c) ₹221 (d) ₹204
23. 23.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
24. 24.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹40 (d) ₹5
25. 25.If 3 notebooks cost ₹72, how much do 11 notebooks cost? (a) ₹792 (b) ₹288 (c) ₹80 (d) ₹264
26. 26.If 4 pens cost ₹68, how much do 9 pens cost? (a) ₹153 (b) ₹73 (c) ₹612 (d) ₹170
27. 27.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 5 days (d) 3 days
28. 28.If 4 kites cost ₹36, how much do 2 kites cost? (a) ₹72 (b) ₹27 (c) ₹34 (d) ₹18
29. 29.If 9 pens cost ₹153, how much do 5 pens cost? (a) ₹102 (b) ₹765 (c) ₹85 (d) ₹149
30. 30.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 17 days (d) 22 days
31. 31.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹168 (b) ₹84 (c) ₹126 (d) ₹42
32. 32.If 4 notebooks cost ₹56, how much do 6 notebooks cost? (a) ₹98 (b) ₹58 (c) ₹336 (d) ₹84
33. 33.If 5 notebooks cost ₹15, how much do 10 notebooks cost? (a) ₹150 (b) ₹33 (c) ₹30 (d) ₹20
34. 34.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹8 (b) ₹64 (c) ₹56 (d) ₹32
35. 35.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 12 days (d) 4 days
36. 36.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 3 days (c) 15 days (d) 37 days
37. 37.If 3 mangoes cost ₹69, how much do 2 mangoes cost? (a) ₹68 (b) ₹69 (c) ₹46 (d) ₹138
38. 38.If 4 pens cost ₹36, how much do 9 pens cost? (a) ₹81 (b) ₹90 (c) ₹41 (d) ₹324
39. 39.If 8 pens cost ₹96, how much do 10 pens cost? (a) ₹132 (b) ₹98 (c) ₹960 (d) ₹120
40. 40.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 5 days (d) 15 days

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