Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 900 · 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.If 2 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹144 (b) ₹252 (c) ₹41 (d) ₹126
2. 2.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹90 (b) ₹60 (c) ₹120 (d) ₹30
3. 3.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
4. 4.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹98 (b) ₹42 (c) ₹14 (d) ₹70
5. 5.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days
6. 6.If 3 mangoes cost ₹21, how much do 8 mangoes cost? (a) ₹168 (b) ₹26 (c) ₹56 (d) ₹63
7. 7.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 13 days (d) 8 days
8. 8.If 3 kites cost ₹60, how much do 6 kites cost? (a) ₹63 (b) ₹120 (c) ₹140 (d) ₹360
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.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹195 (c) ₹273 (d) ₹39
11. 11.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 16 days (d) 15 days
12. 12.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 10 days (d) 28 days
13. 13.If 7 mangoes cost ₹140, how much do 2 mangoes cost? (a) ₹60 (b) ₹280 (c) ₹40 (d) ₹135
14. 14.If 6 kites cost ₹36, how much do 4 kites cost? (a) ₹144 (b) ₹24 (c) ₹30 (d) ₹34
15. 15.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹70 (c) ₹55 (d) ₹10
16. 16.If 7 pens cost ₹35, how much do 6 pens cost? (a) ₹34 (b) ₹30 (c) ₹35 (d) ₹210
17. 17.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 3 days
18. 18.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹56 (b) ₹64 (c) ₹16 (d) ₹48
19. 19.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 12 days (c) 8 days (d) 7 days
20. 20.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 18 days (d) 19 days
21. 21.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹196 (d) ₹147
22. 22.₹297 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹265 (b) ₹297 (c) ₹33 (d) ₹264
23. 23.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 24 days (c) 6 days (d) 16 days
24. 24.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹73 (b) ₹81 (c) ₹72 (d) ₹9
25. 25.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 3 days
26. 26.If 6 pens cost ₹24, how much do 11 pens cost? (a) ₹48 (b) ₹29 (c) ₹264 (d) ₹44
27. 27.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 10 days (c) 16 days (d) 26 days
28. 28.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹13 (b) ₹18 (c) ₹36 (d) ₹24
29. 29.If 6 notebooks cost ₹84, how much do 11 notebooks cost? (a) ₹924 (b) ₹154 (c) ₹168 (d) ₹89
30. 30.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 7 days (d) 6 days
31. 31.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 10 days (d) 14 days
32. 32.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹11 (c) ₹88 (d) ₹33
33. 33.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 15 days (d) 7 days
34. 34.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 26 days (d) 13 days
35. 35.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 16 days (c) 5 days (d) 4 days
36. 36.If 9 kites cost ₹144, how much do 5 kites cost? (a) ₹720 (b) ₹96 (c) ₹80 (d) ₹140
37. 37.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹44 (d) ₹77
38. 38.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 15 days (d) 22 days
39. 39.₹352 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹288 (d) ₹176
40. 40.If 6 mangoes cost ₹90, how much do 9 mangoes cost? (a) ₹135 (b) ₹150 (c) ₹93 (d) ₹810

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