Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 136 · 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.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹207 (b) ₹230 (c) ₹184 (d) ₹46
2. 2.4 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
3. 3.If 7 notebooks cost ₹133, how much do 9 notebooks cost? (a) ₹171 (b) ₹1197 (c) ₹190 (d) ₹135
4. 4.If 8 mangoes cost ₹152, how much do 4 mangoes cost? (a) ₹95 (b) ₹148 (c) ₹76 (d) ₹608
5. 5.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹41 (b) ₹246 (c) ₹205 (d) ₹287
6. 6.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹140 (d) ₹210
7. 7.If 3 kites cost ₹24, how much do 11 kites cost? (a) ₹88 (b) ₹32 (c) ₹96 (d) ₹264
8. 8.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 15 days (c) 8 days (d) 9 days
9. 9.If 6 kites cost ₹114, how much do 3 kites cost? (a) ₹76 (b) ₹342 (c) ₹111 (d) ₹57
10. 10.If 9 pens cost ₹27, how much do 7 pens cost? (a) ₹24 (b) ₹189 (c) ₹25 (d) ₹21
11. 11.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹72 (c) ₹120 (d) ₹24
12. 12.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹68 (b) ₹85 (c) ₹17 (d) ₹102
13. 13.If 4 kites cost ₹28, how much do 2 kites cost? (a) ₹26 (b) ₹56 (c) ₹14 (d) ₹21
14. 14.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 11 days (d) 16 days
15. 15.If 2 pens cost ₹46, how much do 10 pens cost? (a) ₹230 (b) ₹253 (c) ₹54 (d) ₹460
16. 16.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 5 days (d) 6 days
17. 17.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 8 days (d) 7 days
18. 18.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹99 (c) ₹297 (d) ₹264
19. 19.₹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
20. 20.If 6 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹24 (b) ₹96 (c) ₹16 (d) ₹44
21. 21.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹282 (d) ₹329
22. 22.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹204 (b) ₹187 (c) ₹170 (d) ₹34
23. 23.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 5 days (d) 20 days
24. 24.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 5 days (d) 9 days
25. 25.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 40 days (d) 39 days
26. 26.If 7 kites cost ₹154, how much do 12 kites cost? (a) ₹159 (b) ₹286 (c) ₹264 (d) ₹1848
27. 27.If 2 notebooks cost ₹44, how much do 10 notebooks cost? (a) ₹220 (b) ₹52 (c) ₹440 (d) ₹242
28. 28.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹299 (b) ₹46 (c) ₹368 (d) ₹230
29. 29.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 18 days (d) 5 days
30. 30.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 10 days (d) 3 days
31. 31.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹174 (b) ₹58 (c) ₹145 (d) ₹29
32. 32.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 1 day
33. 33.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 14 days (d) 13 days
34. 34.If 2 kites cost ₹16, how much do 3 kites cost? (a) ₹17 (b) ₹32 (c) ₹48 (d) ₹24
35. 35.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 27 days (d) 28 days
36. 36.If 8 pens cost ₹120, how much do 4 pens cost? (a) ₹480 (b) ₹75 (c) ₹60 (d) ₹116
37. 37.If 6 mangoes cost ₹84, how much do 12 mangoes cost? (a) ₹90 (b) ₹1008 (c) ₹182 (d) ₹168
38. 38.If 9 kites cost ₹108, how much do 10 kites cost? (a) ₹120 (b) ₹132 (c) ₹109 (d) ₹1080
39. 39.If 4 notebooks cost ₹24, how much do 10 notebooks cost? (a) ₹30 (b) ₹60 (c) ₹240 (d) ₹66
40. 40.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹279 (b) ₹248 (c) ₹31 (d) ₹249

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