Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 34 · 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 3 mangoes cost ₹15, how much do 11 mangoes cost? (a) ₹55 (b) ₹23 (c) ₹165 (d) ₹60
2. 2.If 3 pens cost ₹66, how much do 7 pens cost? (a) ₹176 (b) ₹70 (c) ₹154 (d) ₹462
3. 3.If 5 mangoes cost ₹70, how much do 3 mangoes cost? (a) ₹42 (b) ₹210 (c) ₹68 (d) ₹56
4. 4.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 3 days
5. 5.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹60 (d) ₹50
6. 6.If 3 pens cost ₹48, how much do 12 pens cost? (a) ₹57 (b) ₹208 (c) ₹576 (d) ₹192
7. 7.If 2 notebooks cost ₹6, how much do 5 notebooks cost? (a) ₹30 (b) ₹18 (c) ₹9 (d) ₹15
8. 8.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹19 (b) ₹152 (c) ₹133 (d) ₹76
9. 9.₹141 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹95 (b) ₹141 (c) ₹47 (d) ₹94
10. 10.₹470 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹47 (b) ₹470 (c) ₹423 (d) ₹235
11. 11.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹150 (b) ₹25 (c) ₹100 (d) ₹125
12. 12.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹165 (b) ₹297 (c) ₹33 (d) ₹264
13. 13.If 8 kites cost ₹72, how much do 10 kites cost? (a) ₹90 (b) ₹74 (c) ₹99 (d) ₹720
14. 14.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹188 (b) ₹329 (c) ₹376 (d) ₹47
15. 15.If 5 kites cost ₹125, how much do 2 kites cost? (a) ₹75 (b) ₹122 (c) ₹50 (d) ₹250
16. 16.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹52 (d) ₹39
17. 17.If 2 mangoes cost ₹50, how much do 8 mangoes cost? (a) ₹400 (b) ₹200 (c) ₹56 (d) ₹225
18. 18.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 9 days (d) 16 days
19. 19.If 7 pens cost ₹168, how much do 10 pens cost? (a) ₹264 (b) ₹171 (c) ₹240 (d) ₹1680
20. 20.If 3 kites cost ₹48, how much do 12 kites cost? (a) ₹576 (b) ₹57 (c) ₹208 (d) ₹192
21. 21.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹117 (d) ₹145
22. 22.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 19 days (d) 18 days
23. 23.If 4 pens cost ₹68, how much do 9 pens cost? (a) ₹170 (b) ₹612 (c) ₹73 (d) ₹153
24. 24.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 42 days (b) 20 days (c) 43 days (d) 8 days
25. 25.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 8 days (d) 7 days
26. 26.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 15 days (d) 27 days
27. 27.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹252 (b) ₹224 (c) ₹28 (d) ₹126
28. 28.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 7 days (d) 6 days
29. 29.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
30. 30.If 6 kites cost ₹90, how much do 7 kites cost? (a) ₹105 (b) ₹91 (c) ₹120 (d) ₹630
31. 31.If 8 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹18 (b) ₹15 (c) ₹120 (d) ₹21
32. 32.If 6 mangoes cost ₹108, how much do 8 mangoes cost? (a) ₹162 (b) ₹864 (c) ₹144 (d) ₹110
33. 33.If 9 notebooks cost ₹117, how much do 12 notebooks cost? (a) ₹1404 (b) ₹156 (c) ₹120 (d) ₹169
34. 34.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹100 (b) ₹160 (c) ₹20 (d) ₹130
35. 35.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 16 days
36. 36.If 3 pens cost ₹12, how much do 6 pens cost? (a) ₹28 (b) ₹72 (c) ₹15 (d) ₹24
37. 37.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 13 days (d) 8 days
38. 38.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹252 (b) ₹112 (c) ₹28 (d) ₹182
39. 39.If 6 kites cost ₹114, how much do 11 kites cost? (a) ₹119 (b) ₹228 (c) ₹209 (d) ₹1254
40. 40.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 13 days (d) 12 days

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