Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 430 · 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.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹279 (b) ₹248 (c) ₹155 (d) ₹31
2. 2.₹216 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹216 (b) ₹180 (c) ₹108 (d) ₹36
3. 3.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 8 days (d) 4 days
4. 4.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 33 days (c) 5 days (d) 34 days
5. 5.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹19 (b) ₹152 (c) ₹95 (d) ₹171
6. 6.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹308 (d) ₹198
7. 7.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹300 (b) ₹50 (c) ₹250 (d) ₹275
8. 8.If 2 pens cost ₹10, how much do 11 pens cost? (a) ₹55 (b) ₹19 (c) ₹110 (d) ₹60
9. 9.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹153 (b) ₹136 (c) ₹51 (d) ₹17
10. 10.If 7 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹28 (b) ₹27 (c) ₹24 (d) ₹168
11. 11.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 22 days (d) 21 days
12. 12.If 8 notebooks cost ₹112, how much do 7 notebooks cost? (a) ₹98 (b) ₹111 (c) ₹112 (d) ₹784
13. 13.If 5 pens cost ₹15, how much do 9 pens cost? (a) ₹27 (b) ₹19 (c) ₹135 (d) ₹30
14. 14.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹350 (d) ₹315
15. 15.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹156 (b) ₹78 (c) ₹117 (d) ₹39
16. 16.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 45 days (c) 17 days (d) 5 days
17. 17.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 17 days (c) 7 days (d) 6 days
18. 18.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹136 (b) ₹102 (c) ₹119 (d) ₹34
19. 19.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 28 days (c) 7 days (d) 10 days
20. 20.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 9 days (d) 8 days
21. 21.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 10 days (d) 28 days
22. 22.If 7 kites cost ₹154, how much do 8 kites cost? (a) ₹176 (b) ₹155 (c) ₹198 (d) ₹1232
23. 23.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 2 days (d) 9 days
24. 24.If 6 pens cost ₹108, how much do 2 pens cost? (a) ₹54 (b) ₹104 (c) ₹216 (d) ₹36
25. 25.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹230 (d) ₹207
26. 26.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹164 (d) ₹123
27. 27.If 3 pens cost ₹51, how much do 12 pens cost? (a) ₹221 (b) ₹204 (c) ₹60 (d) ₹612
28. 28.If 3 kites cost ₹60, how much do 4 kites cost? (a) ₹61 (b) ₹240 (c) ₹80 (d) ₹100
29. 29.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 5 days (d) 16 days
30. 30.If 7 pens cost ₹56, how much do 10 pens cost? (a) ₹560 (b) ₹80 (c) ₹59 (d) ₹88
31. 31.If 4 kites cost ₹52, how much do 10 kites cost? (a) ₹58 (b) ₹130 (c) ₹520 (d) ₹143
32. 32.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹21 (c) ₹7 (d) ₹35
33. 33.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹196 (c) ₹28 (d) ₹252
34. 34.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
35. 35.If 7 mangoes cost ₹105, how much do 2 mangoes cost? (a) ₹30 (b) ₹45 (c) ₹100 (d) ₹210
36. 36.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹102 (d) ₹238
37. 37.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 6 days (d) 7 days
38. 38.If 4 mangoes cost ₹68, how much do 2 mangoes cost? (a) ₹34 (b) ₹66 (c) ₹136 (d) ₹51
39. 39.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹105 (d) ₹90
40. 40.If 6 notebooks cost ₹102, how much do 3 notebooks cost? (a) ₹306 (b) ₹99 (c) ₹51 (d) ₹68

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