Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 904 · 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. 1.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
2. 2.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹344 (d) ₹387
3. 3.If 6 kites cost ₹132, how much do 4 kites cost? (a) ₹130 (b) ₹110 (c) ₹528 (d) ₹88
4. 4.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 10 days (d) 8 days
5. 5.If 3 pens cost ₹9, how much do 5 pens cost? (a) ₹11 (b) ₹18 (c) ₹15 (d) ₹45
6. 6.If 2 pens cost ₹30, how much do 3 pens cost? (a) ₹31 (b) ₹60 (c) ₹45 (d) ₹90
7. 7.If 3 notebooks cost ₹45, how much do 2 notebooks cost? (a) ₹45 (b) ₹30 (c) ₹90 (d) ₹44
8. 8.If 5 pens cost ₹40, how much do 11 pens cost? (a) ₹88 (b) ₹440 (c) ₹46 (d) ₹96
9. 9.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 35 days (c) 11 days (d) 36 days
10. 10.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 15 days (c) 3 days (d) 36 days
11. 11.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 9 days (d) 22 days
12. 12.If 3 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹168 (b) ₹56 (c) ₹70 (d) ₹43
13. 13.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹160 (d) ₹96
14. 14.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹5 (b) ₹50 (c) ₹25 (d) ₹45
15. 15.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 8 days (d) 6 days
16. 16.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
17. 17.If 9 kites cost ₹162, how much do 8 kites cost? (a) ₹161 (b) ₹144 (c) ₹162 (d) ₹1296
18. 18.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹10 (b) ₹15 (c) ₹36 (d) ₹12
19. 19.₹128 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹64 (c) ₹48 (d) ₹16
20. 20.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 13 days (d) 4 days
21. 21.If 2 notebooks cost ₹6, how much do 11 notebooks cost? (a) ₹33 (b) ₹66 (c) ₹36 (d) ₹15
22. 22.If 4 notebooks cost ₹16, how much do 6 notebooks cost? (a) ₹24 (b) ₹18 (c) ₹96 (d) ₹28
23. 23.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹49 (d) ₹35
24. 24.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 7 days
25. 25.If 3 kites cost ₹9, how much do 2 kites cost? (a) ₹9 (b) ₹8 (c) ₹6 (d) ₹18
26. 26.If 9 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹24 (b) ₹216 (c) ₹49 (d) ₹30
27. 27.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹324 (d) ₹288
28. 28.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 3 days (d) 27 days
29. 29.If 9 mangoes cost ₹144, how much do 5 mangoes cost? (a) ₹720 (b) ₹140 (c) ₹96 (d) ₹80
30. 30.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 15 days (d) 6 days
31. 31.If 6 pens cost ₹60, how much do 3 pens cost? (a) ₹40 (b) ₹57 (c) ₹30 (d) ₹180
32. 32.₹120 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹72 (c) ₹60 (d) ₹24
33. 33.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹147 (b) ₹392 (c) ₹441 (d) ₹49
34. 34.If 2 mangoes cost ₹34, how much do 6 mangoes cost? (a) ₹204 (b) ₹119 (c) ₹38 (d) ₹102
35. 35.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 13 days (d) 2 days
36. 36.If 6 mangoes cost ₹144, how much do 3 mangoes cost? (a) ₹72 (b) ₹141 (c) ₹432 (d) ₹96
37. 37.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹387 (b) ₹345 (c) ₹344 (d) ₹43
38. 38.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹138 (d) ₹115
39. 39.If 3 pens cost ₹9, how much do 6 pens cost? (a) ₹12 (b) ₹21 (c) ₹54 (d) ₹18
40. 40.₹235 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹189 (b) ₹47 (c) ₹235 (d) ₹188

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