Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 752 · 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.₹270 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹270 (b) ₹243 (c) ₹135 (d) ₹27
2. 2.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 10 days (d) 9 days
3. 3.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 19 days
4. 4.If 2 kites cost ₹18, how much do 11 kites cost? (a) ₹99 (b) ₹198 (c) ₹108 (d) ₹27
5. 5.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹88 (d) ₹80
6. 6.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹140 (b) ₹20 (c) ₹60 (d) ₹100
7. 7.If 2 pens cost ₹22, how much do 8 pens cost? (a) ₹88 (b) ₹99 (c) ₹28 (d) ₹176
8. 8.₹165 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹120 (b) ₹45 (c) ₹135 (d) ₹15
9. 9.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 10 days (c) 18 days (d) 7 days
10. 10.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹126 (d) ₹108
11. 11.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 39 days (d) 40 days
12. 12.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹126 (b) ₹14 (c) ₹91 (d) ₹56
13. 13.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 11 days
14. 14.If 2 kites cost ₹18, how much do 8 kites cost? (a) ₹72 (b) ₹24 (c) ₹144 (d) ₹81
15. 15.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 7 days
16. 16.If 8 mangoes cost ₹56, how much do 2 mangoes cost? (a) ₹21 (b) ₹14 (c) ₹112 (d) ₹50
17. 17.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹140 (b) ₹20 (c) ₹120 (d) ₹100
18. 18.If 2 mangoes cost ₹10, how much do 5 mangoes cost? (a) ₹13 (b) ₹50 (c) ₹30 (d) ₹25
19. 19.If 9 kites cost ₹207, how much do 4 kites cost? (a) ₹92 (b) ₹828 (c) ₹115 (d) ₹202
20. 20.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 7 days (d) 8 days
21. 21.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 43 days (d) 42 days
22. 22.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 4 days (d) 6 days
23. 23.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹63 (d) ₹9
24. 24.If 3 mangoes cost ₹9, how much do 5 mangoes cost? (a) ₹45 (b) ₹18 (c) ₹11 (d) ₹15
25. 25.If 7 kites cost ₹98, how much do 2 kites cost? (a) ₹28 (b) ₹196 (c) ₹93 (d) ₹42
26. 26.If 5 pens cost ₹100, how much do 3 pens cost? (a) ₹98 (b) ₹300 (c) ₹60 (d) ₹80
27. 27.If 9 pens cost ₹171, how much do 4 pens cost? (a) ₹76 (b) ₹684 (c) ₹166 (d) ₹95
28. 28.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 2 days (d) 3 days
29. 29.3 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) 4 days (d) 7 days
30. 30.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹45 (b) ₹11 (c) ₹55 (d) ₹44
31. 31.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹32 (d) ₹24
32. 32.If 4 notebooks cost ₹92, how much do 5 notebooks cost? (a) ₹460 (b) ₹115 (c) ₹93 (d) ₹138
33. 33.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 7 days (c) 32 days (d) 17 days
34. 34.₹77 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹11 (b) ₹67 (c) ₹77 (d) ₹66
35. 35.If 9 notebooks cost ₹225, how much do 7 notebooks cost? (a) ₹200 (b) ₹1575 (c) ₹223 (d) ₹175
36. 36.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 11 days (c) 15 days (d) 27 days
37. 37.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹52 (b) ₹130 (c) ₹117 (d) ₹13
38. 38.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹25 (b) ₹20 (c) ₹16 (d) ₹60
39. 39.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 9 days (d) 2 days
40. 40.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 11 days (d) 21 days

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