Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 362 · 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 5 kites cost ₹100, how much do 12 kites cost? (a) ₹260 (b) ₹240 (c) ₹1200 (d) ₹107
2. 2.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 6 days (d) 7 days
3. 3.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 7 days (d) 9 days
4. 4.If 6 kites cost ₹150, how much do 9 kites cost? (a) ₹153 (b) ₹250 (c) ₹225 (d) ₹1350
5. 5.If 7 notebooks cost ₹77, how much do 12 notebooks cost? (a) ₹924 (b) ₹143 (c) ₹82 (d) ₹132
6. 6.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 26 days (d) 17 days
7. 7.If 4 kites cost ₹52, how much do 7 kites cost? (a) ₹364 (b) ₹104 (c) ₹91 (d) ₹55
8. 8.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
9. 9.If 3 notebooks cost ₹27, how much do 2 notebooks cost? (a) ₹18 (b) ₹26 (c) ₹54 (d) ₹27
10. 10.If 7 mangoes cost ₹77, how much do 12 mangoes cost? (a) ₹143 (b) ₹924 (c) ₹82 (d) ₹132
11. 11.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹60 (c) ₹90 (d) ₹30
12. 12.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 7 days (d) 52 days
13. 13.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹145 (b) ₹203 (c) ₹29 (d) ₹261
14. 14.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹54 (b) ₹81 (c) ₹108 (d) ₹27
15. 15.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 9 days (d) 8 days
16. 16.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹150 (d) ₹135
17. 17.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 11 days (d) 7 days
18. 18.If 2 pens cost ₹50, how much do 3 pens cost? (a) ₹51 (b) ₹150 (c) ₹75 (d) ₹100
19. 19.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
20. 20.If 4 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹42 (b) ₹55 (c) ₹168 (d) ₹56
21. 21.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 8 days (d) 9 days
22. 22.If 3 mangoes cost ₹60, how much do 4 mangoes cost? (a) ₹80 (b) ₹240 (c) ₹61 (d) ₹100
23. 23.If 7 mangoes cost ₹35, how much do 6 mangoes cost? (a) ₹34 (b) ₹30 (c) ₹35 (d) ₹210
24. 24.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 22 days (d) 21 days
25. 25.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹108 (b) ₹162 (c) ₹27 (d) ₹135
26. 26.If 9 mangoes cost ₹207, how much do 4 mangoes cost? (a) ₹92 (b) ₹202 (c) ₹828 (d) ₹115
27. 27.If 3 pens cost ₹45, how much do 5 pens cost? (a) ₹47 (b) ₹225 (c) ₹75 (d) ₹90
28. 28.If 8 mangoes cost ₹112, how much do 12 mangoes cost? (a) ₹168 (b) ₹182 (c) ₹116 (d) ₹1344
29. 29.If 9 notebooks cost ₹207, how much do 8 notebooks cost? (a) ₹1656 (b) ₹206 (c) ₹184 (d) ₹207
30. 30.If 2 pens cost ₹20, how much do 7 pens cost? (a) ₹80 (b) ₹140 (c) ₹25 (d) ₹70
31. 31.If 2 mangoes cost ₹46, how much do 9 mangoes cost? (a) ₹53 (b) ₹414 (c) ₹230 (d) ₹207
32. 32.If 7 pens cost ₹140, how much do 12 pens cost? (a) ₹1680 (b) ₹260 (c) ₹240 (d) ₹145
33. 33.If 6 kites cost ₹126, how much do 4 kites cost? (a) ₹84 (b) ₹504 (c) ₹105 (d) ₹124
34. 34.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹175 (b) ₹50 (c) ₹200 (d) ₹25
35. 35.If 7 pens cost ₹161, how much do 11 pens cost? (a) ₹165 (b) ₹276 (c) ₹253 (d) ₹1771
36. 36.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹60 (b) ₹120 (c) ₹24 (d) ₹96
37. 37.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹18 (c) ₹54 (d) ₹90
38. 38.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹49 (b) ₹441 (c) ₹393 (d) ₹392
39. 39.₹96 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹84 (b) ₹96 (c) ₹48 (d) ₹12
40. 40.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 18 days (d) 10 days

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