Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 807 · 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 7 mangoes cost ₹140, how much do 3 mangoes cost? (a) ₹420 (b) ₹80 (c) ₹136 (d) ₹60
2. 2.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹57 (d) ₹38
3. 3.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹110 (b) ₹154 (c) ₹198 (d) ₹22
4. 4.If 8 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹360 (b) ₹50 (c) ₹45 (d) ₹41
5. 5.If 4 kites cost ₹20, how much do 5 kites cost? (a) ₹25 (b) ₹30 (c) ₹21 (d) ₹100
6. 6.If 2 notebooks cost ₹50, how much do 8 notebooks cost? (a) ₹400 (b) ₹56 (c) ₹225 (d) ₹200
7. 7.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹165 (d) ₹164
8. 8.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 19 days (c) 18 days (d) 16 days
9. 9.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 9 days (d) 13 days
10. 10.If 2 kites cost ₹44, how much do 8 kites cost? (a) ₹176 (b) ₹352 (c) ₹198 (d) ₹50
11. 11.If 4 notebooks cost ₹40, how much do 5 notebooks cost? (a) ₹41 (b) ₹50 (c) ₹200 (d) ₹60
12. 12.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹168 (d) ₹240
13. 13.If 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹81 (b) ₹720 (c) ₹90 (d) ₹100
14. 14.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹145 (b) ₹261 (c) ₹29 (d) ₹290
15. 15.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹20 (b) ₹110 (c) ₹100 (d) ₹120
16. 16.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 5 days (d) 13 days
17. 17.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 4 days
18. 18.₹225 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹225 (b) ₹180 (c) ₹45 (d) ₹181
19. 19.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day
20. 20.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 9 days (d) 3 days
21. 21.If 9 mangoes cost ₹135, how much do 6 mangoes cost? (a) ₹105 (b) ₹810 (c) ₹90 (d) ₹132
22. 22.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹232 (b) ₹29 (c) ₹261 (d) ₹145
23. 23.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 3 days (d) 1 day
24. 24.If 2 notebooks cost ₹44, how much do 7 notebooks cost? (a) ₹154 (b) ₹176 (c) ₹49 (d) ₹308
25. 25.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹210 (b) ₹420 (c) ₹42 (d) ₹378
26. 26.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹105 (b) ₹140 (c) ₹175 (d) ₹35
27. 27.If 7 notebooks cost ₹56, how much do 12 notebooks cost? (a) ₹61 (b) ₹672 (c) ₹104 (d) ₹96
28. 28.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 20 days (c) 56 days (d) 8 days
29. 29.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹119 (b) ₹204 (c) ₹238 (d) ₹34
30. 30.If 3 kites cost ₹39, how much do 12 kites cost? (a) ₹156 (b) ₹169 (c) ₹48 (d) ₹468
31. 31.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 14 days (d) 20 days
32. 32.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹132 (b) ₹231 (c) ₹33 (d) ₹264
33. 33.If 4 mangoes cost ₹32, how much do 5 mangoes cost? (a) ₹48 (b) ₹40 (c) ₹33 (d) ₹160
34. 34.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 15 days (d) 8 days
35. 35.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 27 days (c) 26 days (d) 28 days
36. 36.8 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
37. 37.If 8 notebooks cost ₹192, how much do 10 notebooks cost? (a) ₹240 (b) ₹264 (c) ₹1920 (d) ₹194
38. 38.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
39. 39.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 4 days (d) 3 days
40. 40.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹72 (d) ₹24

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