Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 473 · 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. 1.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 1 day (d) 13 days
2. 2.If 9 pens cost ₹54, how much do 12 pens cost? (a) ₹57 (b) ₹72 (c) ₹78 (d) ₹648
3. 3.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 13 days
4. 4.If 6 pens cost ₹60, how much do 9 pens cost? (a) ₹90 (b) ₹63 (c) ₹100 (d) ₹540
5. 5.If 6 notebooks cost ₹126, how much do 9 notebooks cost? (a) ₹189 (b) ₹129 (c) ₹210 (d) ₹1134
6. 6.₹217 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹187 (b) ₹217 (c) ₹186 (d) ₹31
7. 7.If 8 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹35 (b) ₹120 (c) ₹15 (d) ₹20
8. 8.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 1 day (d) 10 days
9. 9.If 5 notebooks cost ₹55, how much do 4 notebooks cost? (a) ₹44 (b) ₹54 (c) ₹55 (d) ₹220
10. 10.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 17 days (d) 27 days
11. 11.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹34 (b) ₹51 (c) ₹68 (d) ₹17
12. 12.If 4 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹45 (b) ₹55 (c) ₹66 (d) ₹220
13. 13.If 7 notebooks cost ₹21, how much do 12 notebooks cost? (a) ₹26 (b) ₹252 (c) ₹39 (d) ₹36
14. 14.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹132 (b) ₹44 (c) ₹176 (d) ₹154
15. 15.If 3 pens cost ₹36, how much do 12 pens cost? (a) ₹156 (b) ₹432 (c) ₹144 (d) ₹45
16. 16.If 2 kites cost ₹16, how much do 3 kites cost? (a) ₹17 (b) ₹48 (c) ₹32 (d) ₹24
17. 17.If 2 pens cost ₹20, how much do 8 pens cost? (a) ₹26 (b) ₹80 (c) ₹160 (d) ₹90
18. 18.If 2 notebooks cost ₹26, how much do 3 notebooks cost? (a) ₹78 (b) ₹52 (c) ₹27 (d) ₹39
19. 19.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 11 days (d) 15 days
20. 20.If 3 pens cost ₹72, how much do 9 pens cost? (a) ₹78 (b) ₹240 (c) ₹216 (d) ₹648
21. 21.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹78 (b) ₹48 (c) ₹108 (d) ₹12
22. 22.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹112 (b) ₹63 (c) ₹14 (d) ₹126
23. 23.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 27 days (d) 15 days
24. 24.If 6 pens cost ₹72, how much do 3 pens cost? (a) ₹216 (b) ₹69 (c) ₹48 (d) ₹36
25. 25.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 10 days (d) 3 days
26. 26.If 4 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹48 (b) ₹144 (c) ₹36 (d) ₹47
27. 27.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 8 days
28. 28.If 3 kites cost ₹54, how much do 5 kites cost? (a) ₹56 (b) ₹270 (c) ₹108 (d) ₹90
29. 29.If 9 notebooks cost ₹144, how much do 10 notebooks cost? (a) ₹145 (b) ₹176 (c) ₹1440 (d) ₹160
30. 30.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹161 (b) ₹115 (c) ₹138 (d) ₹23
31. 31.₹240 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹30 (b) ₹210 (c) ₹120 (d) ₹240
32. 32.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 7 days
33. 33.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹54 (b) ₹306 (c) ₹102 (d) ₹119
34. 34.If 5 notebooks cost ₹90, how much do 6 notebooks cost? (a) ₹91 (b) ₹108 (c) ₹540 (d) ₹126
35. 35.If 4 pens cost ₹84, how much do 3 pens cost? (a) ₹83 (b) ₹84 (c) ₹252 (d) ₹63
36. 36.If 5 notebooks cost ₹90, how much do 9 notebooks cost? (a) ₹180 (b) ₹810 (c) ₹162 (d) ₹94
37. 37.If 6 mangoes cost ₹78, how much do 11 mangoes cost? (a) ₹83 (b) ₹143 (c) ₹156 (d) ₹858
38. 38.If 7 kites cost ₹98, how much do 11 kites cost? (a) ₹154 (b) ₹102 (c) ₹168 (d) ₹1078
39. 39.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 5 days
40. 40.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 10 days (d) 18 days

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