Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 580 · 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.₹500 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹350 (b) ₹150 (c) ₹250 (d) ₹50
2. 2.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
3. 3.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 12 days (d) 4 days
4. 4.If 7 notebooks cost ₹126, how much do 11 notebooks cost? (a) ₹1386 (b) ₹198 (c) ₹216 (d) ₹130
5. 5.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 28 days (d) 18 days
6. 6.If 7 kites cost ₹119, how much do 8 kites cost? (a) ₹120 (b) ₹136 (c) ₹952 (d) ₹153
7. 7.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 1 day
8. 8.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 23 days (c) 22 days (d) 15 days
9. 9.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 28 days (d) 19 days
10. 10.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹24 (b) ₹30 (c) ₹15 (d) ₹6
11. 11.₹88 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹44 (c) ₹66 (d) ₹22
12. 12.₹451 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹328 (b) ₹123 (c) ₹41 (d) ₹369
13. 13.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 17 days (c) 11 days (d) 36 days
14. 14.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹420 (b) ₹42 (c) ₹378 (d) ₹210
15. 15.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹150 (d) ₹135
16. 16.If 2 mangoes cost ₹18, how much do 11 mangoes cost? (a) ₹108 (b) ₹27 (c) ₹99 (d) ₹198
17. 17.₹270 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹243 (b) ₹135 (c) ₹27 (d) ₹270
18. 18.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 7 days (c) 53 days (d) 19 days
19. 19.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 4 days (d) 10 days
20. 20.If 7 mangoes cost ₹35, how much do 2 mangoes cost? (a) ₹10 (b) ₹15 (c) ₹30 (d) ₹70
21. 21.If 4 kites cost ₹24, how much do 2 kites cost? (a) ₹48 (b) ₹22 (c) ₹18 (d) ₹12
22. 22.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹15 (c) ₹60 (d) ₹75
23. 23.If 5 kites cost ₹55, how much do 6 kites cost? (a) ₹330 (b) ₹66 (c) ₹56 (d) ₹77
24. 24.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 5 days
25. 25.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 5 days (c) 16 days (d) 4 days
26. 26.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 2 days
27. 27.If 7 pens cost ₹28, how much do 10 pens cost? (a) ₹31 (b) ₹44 (c) ₹40 (d) ₹280
28. 28.If 6 kites cost ₹150, how much do 9 kites cost? (a) ₹250 (b) ₹225 (c) ₹1350 (d) ₹153
29. 29.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹126 (b) ₹18 (c) ₹144 (d) ₹72
30. 30.If 4 pens cost ₹40, how much do 3 pens cost? (a) ₹120 (b) ₹40 (c) ₹30 (d) ₹39
31. 31.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹198 (d) ₹143
32. 32.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹231 (c) ₹252 (d) ₹210
33. 33.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 7 days (d) 6 days
34. 34.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 12 days (d) 6 days
35. 35.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹16 (d) ₹20
36. 36.If 3 pens cost ₹42, how much do 10 pens cost? (a) ₹154 (b) ₹140 (c) ₹49 (d) ₹420
37. 37.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹230 (d) ₹138
38. 38.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 10 days (d) 5 days
39. 39.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 61 days (b) 60 days (c) 21 days (d) 9 days
40. 40.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 30 days (c) 31 days (d) 17 days

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