Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 682 · 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 4 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹126 (b) ₹108 (c) ₹432 (d) ₹74
2. 2.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 4 days (d) 3 days
3. 3.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹235 (b) ₹329 (c) ₹47 (d) ₹141
4. 4.If 6 mangoes cost ₹66, how much do 4 mangoes cost? (a) ₹64 (b) ₹44 (c) ₹264 (d) ₹55
5. 5.If 7 kites cost ₹91, how much do 4 kites cost? (a) ₹65 (b) ₹364 (c) ₹52 (d) ₹88
6. 6.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 8 days (d) 7 days
7. 7.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 7 days (d) 9 days
8. 8.If 9 pens cost ₹198, how much do 7 pens cost? (a) ₹1386 (b) ₹154 (c) ₹196 (d) ₹176
9. 9.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹174 (d) ₹145
10. 10.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹272 (b) ₹306 (c) ₹153 (d) ₹34
11. 11.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹105 (b) ₹35 (c) ₹70 (d) ₹140
12. 12.If 2 pens cost ₹10, how much do 4 pens cost? (a) ₹25 (b) ₹20 (c) ₹12 (d) ₹40
13. 13.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 3 days (d) 4 days
14. 14.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹48 (b) ₹13 (c) ₹16 (d) ₹20
15. 15.₹90 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹9 (d) ₹81
16. 16.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 36 days (c) 6 days (d) 4 days
17. 17.If 9 kites cost ₹225, how much do 11 kites cost? (a) ₹2475 (b) ₹300 (c) ₹227 (d) ₹275
18. 18.If 9 kites cost ₹72, how much do 10 kites cost? (a) ₹88 (b) ₹720 (c) ₹80 (d) ₹73
19. 19.If 8 pens cost ₹96, how much do 11 pens cost? (a) ₹144 (b) ₹99 (c) ₹1056 (d) ₹132
20. 20.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹47 (b) ₹94 (c) ₹188 (d) ₹141
21. 21.If 9 notebooks cost ₹207, how much do 5 notebooks cost? (a) ₹138 (b) ₹203 (c) ₹1035 (d) ₹115
22. 22.If 2 pens cost ₹22, how much do 12 pens cost? (a) ₹143 (b) ₹32 (c) ₹264 (d) ₹132
23. 23.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹84 (b) ₹105 (c) ₹64 (d) ₹252
24. 24.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹33 (d) ₹55
25. 25.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹110 (b) ₹44 (c) ₹99 (d) ₹11
26. 26.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
27. 27.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 8 days (d) 7 days
28. 28.If 8 kites cost ₹80, how much do 12 kites cost? (a) ₹84 (b) ₹120 (c) ₹960 (d) ₹130
29. 29.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹120 (b) ₹12 (c) ₹108 (d) ₹60
30. 30.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹88 (d) ₹77
31. 31.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
32. 32.If 7 kites cost ₹112, how much do 5 kites cost? (a) ₹560 (b) ₹96 (c) ₹80 (d) ₹110
33. 33.If 5 mangoes cost ₹45, how much do 11 mangoes cost? (a) ₹108 (b) ₹99 (c) ₹495 (d) ₹51
34. 34.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹283 (b) ₹282 (c) ₹47 (d) ₹329
35. 35.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
36. 36.If 4 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹28 (b) ₹54 (c) ₹192 (d) ₹48
37. 37.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹14 (d) ₹98
38. 38.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
39. 39.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 14 days (d) 15 days
40. 40.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹54 (b) ₹9 (c) ₹63 (d) ₹45

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