Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 273 · 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.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹126 (d) ₹42
2. 2.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹216 (b) ₹156 (c) ₹24 (d) ₹96
3. 3.If 3 kites cost ₹69, how much do 2 kites cost? (a) ₹69 (b) ₹68 (c) ₹46 (d) ₹138
4. 4.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 32 days (d) 33 days
5. 5.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 27 days (d) 19 days
6. 6.If 4 mangoes cost ₹12, how much do 8 mangoes cost? (a) ₹27 (b) ₹16 (c) ₹96 (d) ₹24
7. 7.If 6 pens cost ₹84, how much do 9 pens cost? (a) ₹756 (b) ₹126 (c) ₹140 (d) ₹87
8. 8.If 7 mangoes cost ₹133, how much do 6 mangoes cost? (a) ₹798 (b) ₹132 (c) ₹133 (d) ₹114
9. 9.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 13 days (d) 12 days
10. 10.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 17 days (d) 11 days
11. 11.If 7 kites cost ₹119, how much do 12 kites cost? (a) ₹1428 (b) ₹221 (c) ₹124 (d) ₹204
12. 12.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 28 days (d) 29 days
13. 13.If 2 mangoes cost ₹14, how much do 11 mangoes cost? (a) ₹23 (b) ₹84 (c) ₹154 (d) ₹77
14. 14.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 3 days (d) 28 days
15. 15.If 5 mangoes cost ₹70, how much do 12 mangoes cost? (a) ₹182 (b) ₹840 (c) ₹77 (d) ₹168
16. 16.If 4 kites cost ₹16, how much do 5 kites cost? (a) ₹80 (b) ₹20 (c) ₹17 (d) ₹24
17. 17.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹133 (d) ₹152
18. 18.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 13 days (d) 22 days
19. 19.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 19 days (d) 18 days
20. 20.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 19 days (d) 14 days
21. 21.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹35 (d) ₹42
22. 22.If 3 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹108 (b) ₹54 (c) ₹53 (d) ₹36
23. 23.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹18 (c) ₹24 (d) ₹36
24. 24.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 7 days (d) 3 days
25. 25.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 16 days (d) 10 days
26. 26.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 7 days (d) 8 days
27. 27.If 9 kites cost ₹117, how much do 7 kites cost? (a) ₹819 (b) ₹104 (c) ₹91 (d) ₹115
28. 28.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹40 (b) ₹360 (c) ₹400 (d) ₹200
29. 29.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 11 days (c) 7 days (d) 5 days
30. 30.If 5 kites cost ₹25, how much do 10 kites cost? (a) ₹30 (b) ₹55 (c) ₹250 (d) ₹50
31. 31.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹200 (b) ₹225 (c) ₹201 (d) ₹25
32. 32.If 5 kites cost ₹80, how much do 6 kites cost? (a) ₹96 (b) ₹112 (c) ₹81 (d) ₹480
33. 33.If 7 kites cost ₹154, how much do 2 kites cost? (a) ₹149 (b) ₹308 (c) ₹66 (d) ₹44
34. 34.If 2 kites cost ₹38, how much do 8 kites cost? (a) ₹44 (b) ₹171 (c) ₹304 (d) ₹152
35. 35.₹200 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹40 (b) ₹100 (c) ₹80 (d) ₹120
36. 36.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹70 (b) ₹28 (c) ₹49 (d) ₹14
37. 37.If 7 notebooks cost ₹21, how much do 6 notebooks cost? (a) ₹20 (b) ₹126 (c) ₹21 (d) ₹18
38. 38.If 3 kites cost ₹75, how much do 10 kites cost? (a) ₹275 (b) ₹750 (c) ₹82 (d) ₹250
39. 39.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹65 (b) ₹40 (c) ₹10 (d) ₹90
40. 40.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹170 (b) ₹340 (c) ₹34 (d) ₹306

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