Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 375 · 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. 1.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
2. 2.If 9 kites cost ₹126, how much do 8 kites cost? (a) ₹1008 (b) ₹112 (c) ₹125 (d) ₹126
3. 3.If 8 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹96 (b) ₹12 (c) ₹20 (d) ₹15
4. 4.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 11 days
5. 5.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
6. 6.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹72 (b) ₹96 (c) ₹49 (d) ₹144
7. 7.If 2 pens cost ₹14, how much do 3 pens cost? (a) ₹15 (b) ₹28 (c) ₹42 (d) ₹21
8. 8.If 6 pens cost ₹132, how much do 8 pens cost? (a) ₹198 (b) ₹1056 (c) ₹176 (d) ₹134
9. 9.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 7 days (d) 8 days
10. 10.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹135 (b) ₹105 (c) ₹75 (d) ₹15
11. 11.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 6 days
12. 12.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
13. 13.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 27 days (d) 11 days
14. 14.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 21 days (c) 10 days (d) 20 days
15. 15.₹150 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹75 (b) ₹105 (c) ₹15 (d) ₹45
16. 16.If 3 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹80 (b) ₹64 (c) ₹49 (d) ₹192
17. 17.If 2 mangoes cost ₹38, how much do 3 mangoes cost? (a) ₹39 (b) ₹57 (c) ₹114 (d) ₹76
18. 18.If 9 mangoes cost ₹216, how much do 8 mangoes cost? (a) ₹216 (b) ₹215 (c) ₹1728 (d) ₹192
19. 19.If 2 mangoes cost ₹22, how much do 3 mangoes cost? (a) ₹33 (b) ₹66 (c) ₹44 (d) ₹23
20. 20.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹242 (d) ₹264
21. 21.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 5 days (d) 6 days
22. 22.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹84 (d) ₹98
23. 23.If 4 notebooks cost ₹64, how much do 12 notebooks cost? (a) ₹72 (b) ₹192 (c) ₹768 (d) ₹208
24. 24.₹637 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹196 (b) ₹441 (c) ₹49 (d) ₹490
25. 25.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹9 (d) ₹18
26. 26.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹234 (b) ₹195 (c) ₹39 (d) ₹273
27. 27.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹22 (b) ₹77 (c) ₹154 (d) ₹132
28. 28.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹42 (c) ₹48 (d) ₹12
29. 29.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹22 (b) ₹99 (c) ₹110 (d) ₹88
30. 30.If 8 kites cost ₹168, how much do 5 kites cost? (a) ₹165 (b) ₹840 (c) ₹105 (d) ₹126
31. 31.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹24 (d) ₹16
32. 32.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹25 (b) ₹151 (c) ₹175 (d) ₹150
33. 33.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹18 (c) ₹21 (d) ₹6
34. 34.If 2 pens cost ₹28, how much do 7 pens cost? (a) ₹196 (b) ₹112 (c) ₹33 (d) ₹98
35. 35.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹279 (d) ₹155
36. 36.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 5 days (d) 4 days
37. 37.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 7 days (d) 10 days
38. 38.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹264 (b) ₹33 (c) ₹231 (d) ₹132
39. 39.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹132 (d) ₹110
40. 40.If 3 pens cost ₹24, how much do 12 pens cost? (a) ₹33 (b) ₹288 (c) ₹104 (d) ₹96

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