Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 639 · 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.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹168 (b) ₹210 (c) ₹126 (d) ₹42
2. 2.If 8 kites cost ₹184, how much do 9 kites cost? (a) ₹1656 (b) ₹185 (c) ₹207 (d) ₹230
3. 3.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 8 days (d) 10 days
4. 4.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 7 days (d) 28 days
5. 5.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 10 days (d) 7 days
6. 6.If 4 kites cost ₹84, how much do 12 kites cost? (a) ₹1008 (b) ₹92 (c) ₹273 (d) ₹252
7. 7.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹12 (b) ₹78 (c) ₹96 (d) ₹60
8. 8.If 2 pens cost ₹36, how much do 8 pens cost? (a) ₹42 (b) ₹288 (c) ₹162 (d) ₹144
9. 9.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹35 (b) ₹70 (c) ₹280 (d) ₹245
10. 10.If 3 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹22 (b) ₹84 (c) ₹35 (d) ₹28
11. 11.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 4 days (d) 9 days
12. 12.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹70 (d) ₹30
13. 13.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 7 days (d) 8 days
14. 14.If 5 pens cost ₹85, how much do 12 pens cost? (a) ₹92 (b) ₹1020 (c) ₹221 (d) ₹204
15. 15.If 6 kites cost ₹42, how much do 2 kites cost? (a) ₹84 (b) ₹21 (c) ₹38 (d) ₹14
16. 16.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹189 (b) ₹243 (c) ₹135 (d) ₹27
17. 17.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹154 (b) ₹44 (c) ₹88 (d) ₹220
18. 18.3 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) 4 days (d) 2 days
19. 19.₹341 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹279 (b) ₹31 (c) ₹310 (d) ₹62
20. 20.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 9 days (c) 39 days (d) 17 days
21. 21.If 6 kites cost ₹90, how much do 2 kites cost? (a) ₹45 (b) ₹86 (c) ₹30 (d) ₹180
22. 22.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 43 days (c) 7 days (d) 42 days
23. 23.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 2 days (d) 1 day
24. 24.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹51 (b) ₹68 (c) ₹85 (d) ₹17
25. 25.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 12 days (d) 18 days
26. 26.If 9 pens cost ₹126, how much do 10 pens cost? (a) ₹127 (b) ₹1260 (c) ₹154 (d) ₹140
27. 27.If 9 mangoes cost ₹144, how much do 8 mangoes cost? (a) ₹1152 (b) ₹144 (c) ₹128 (d) ₹143
28. 28.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 3 days
29. 29.If 7 pens cost ₹112, how much do 12 pens cost? (a) ₹192 (b) ₹1344 (c) ₹117 (d) ₹208
30. 30.If 5 pens cost ₹35, how much do 12 pens cost? (a) ₹91 (b) ₹420 (c) ₹84 (d) ₹42
31. 31.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 5 days (d) 4 days
32. 32.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹400 (b) ₹50 (c) ₹350 (d) ₹200
33. 33.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 16 days (d) 12 days
34. 34.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹315 (b) ₹270 (c) ₹225 (d) ₹45
35. 35.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹33 (d) ₹22
36. 36.If 2 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹80 (b) ₹120 (c) ₹41 (d) ₹60
37. 37.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
38. 38.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 16 days (d) 8 days
39. 39.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹26 (b) ₹104 (c) ₹78 (d) ₹130
40. 40.If 4 kites cost ₹36, how much do 5 kites cost? (a) ₹54 (b) ₹37 (c) ₹180 (d) ₹45

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