Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 739 · 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. 1.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 17 days (d) 9 days
2. 2.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹32 (c) ₹40 (d) ₹8
3. 3.If 5 mangoes cost ₹90, how much do 6 mangoes cost? (a) ₹126 (b) ₹540 (c) ₹91 (d) ₹108
4. 4.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹160 (d) ₹140
5. 5.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 4 days (d) 8 days
6. 6.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 19 days (d) 39 days
7. 7.If 5 pens cost ₹100, how much do 4 pens cost? (a) ₹99 (b) ₹100 (c) ₹400 (d) ₹80
8. 8.If 8 pens cost ₹136, how much do 6 pens cost? (a) ₹134 (b) ₹119 (c) ₹102 (d) ₹816
9. 9.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
10. 10.If 5 mangoes cost ₹65, how much do 12 mangoes cost? (a) ₹156 (b) ₹169 (c) ₹72 (d) ₹780
11. 11.If 4 pens cost ₹100, how much do 5 pens cost? (a) ₹500 (b) ₹150 (c) ₹101 (d) ₹125
12. 12.If 9 pens cost ₹153, how much do 6 pens cost? (a) ₹102 (b) ₹119 (c) ₹918 (d) ₹150
13. 13.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹168 (b) ₹48 (c) ₹288 (d) ₹336
14. 14.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹180 (b) ₹288 (c) ₹234 (d) ₹36
15. 15.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹250 (c) ₹50 (d) ₹100
16. 16.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 6 days (d) 10 days
17. 17.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹188 (b) ₹235 (c) ₹47 (d) ₹141
18. 18.If 6 kites cost ₹102, how much do 12 kites cost? (a) ₹1224 (b) ₹221 (c) ₹204 (d) ₹108
19. 19.If 8 kites cost ₹56, how much do 3 kites cost? (a) ₹21 (b) ₹28 (c) ₹51 (d) ₹168
20. 20.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 12 days (d) 9 days
21. 21.If 9 kites cost ₹27, how much do 2 kites cost? (a) ₹54 (b) ₹20 (c) ₹6 (d) ₹9
22. 22.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹245 (d) ₹210
23. 23.If 2 notebooks cost ₹50, how much do 3 notebooks cost? (a) ₹100 (b) ₹150 (c) ₹51 (d) ₹75
24. 24.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 4 days (d) 2 days
25. 25.₹133 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹115 (b) ₹19 (c) ₹114 (d) ₹133
26. 26.If 4 mangoes cost ₹16, how much do 6 mangoes cost? (a) ₹28 (b) ₹18 (c) ₹96 (d) ₹24
27. 27.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹143 (d) ₹182
28. 28.If 7 mangoes cost ₹112, how much do 8 mangoes cost? (a) ₹113 (b) ₹128 (c) ₹144 (d) ₹896
29. 29.₹140 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹100 (d) ₹70
30. 30.₹186 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹155 (d) ₹186
31. 31.If 6 kites cost ₹72, how much do 3 kites cost? (a) ₹48 (b) ₹36 (c) ₹69 (d) ₹216
32. 32.If 7 notebooks cost ₹98, how much do 12 notebooks cost? (a) ₹182 (b) ₹168 (c) ₹103 (d) ₹1176
33. 33.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹14 (b) ₹126 (c) ₹56 (d) ₹91
34. 34.If 7 pens cost ₹154, how much do 5 pens cost? (a) ₹152 (b) ₹110 (c) ₹132 (d) ₹770
35. 35.If 6 mangoes cost ₹150, how much do 7 mangoes cost? (a) ₹1050 (b) ₹200 (c) ₹151 (d) ₹175
36. 36.If 7 pens cost ₹56, how much do 2 pens cost? (a) ₹112 (b) ₹51 (c) ₹16 (d) ₹24
37. 37.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 9 days (d) 5 days
38. 38.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹40 (b) ₹35 (c) ₹10 (d) ₹30
39. 39.If 3 kites cost ₹51, how much do 9 kites cost? (a) ₹170 (b) ₹459 (c) ₹57 (d) ₹153
40. 40.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 28 days (c) 19 days (d) 7 days

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