Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 315 · 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. 1.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 8 days (d) 9 days
2. 2.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 1 day (d) 11 days
3. 3.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
4. 4.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 4 days (d) 9 days
5. 5.If 7 pens cost ₹56, how much do 8 pens cost? (a) ₹72 (b) ₹448 (c) ₹57 (d) ₹64
6. 6.If 9 kites cost ₹180, how much do 4 kites cost? (a) ₹720 (b) ₹175 (c) ₹80 (d) ₹100
7. 7.If 5 notebooks cost ₹80, how much do 6 notebooks cost? (a) ₹81 (b) ₹480 (c) ₹112 (d) ₹96
8. 8.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹155 (b) ₹217 (c) ₹186 (d) ₹31
9. 9.If 5 mangoes cost ₹115, how much do 10 mangoes cost? (a) ₹1150 (b) ₹230 (c) ₹253 (d) ₹120
10. 10.If 9 mangoes cost ₹27, how much do 2 mangoes cost? (a) ₹54 (b) ₹20 (c) ₹9 (d) ₹6
11. 11.If 8 pens cost ₹80, how much do 7 pens cost? (a) ₹560 (b) ₹70 (c) ₹79 (d) ₹80
12. 12.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹60 (d) ₹48
13. 13.If 4 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹440 (b) ₹47 (c) ₹110 (d) ₹120
14. 14.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹400 (b) ₹200 (c) ₹40 (d) ₹360
15. 15.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 14 days (d) 2 days
16. 16.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 18 days (d) 6 days
17. 17.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹20 (d) ₹35
18. 18.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹264 (b) ₹297 (c) ₹165 (d) ₹33
19. 19.₹133 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹19 (b) ₹76 (c) ₹57 (d) ₹95
20. 20.₹217 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹186 (b) ₹31 (c) ₹217 (d) ₹187
21. 21.If 3 pens cost ₹15, how much do 6 pens cost? (a) ₹18 (b) ₹90 (c) ₹35 (d) ₹30
22. 22.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹161 (d) ₹184
23. 23.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 19 days (c) 2 days (d) 18 days
24. 24.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 4 days (d) 36 days
25. 25.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 11 days (d) 26 days
26. 26.If 5 mangoes cost ₹80, how much do 2 mangoes cost? (a) ₹77 (b) ₹32 (c) ₹160 (d) ₹48
27. 27.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 12 days (d) 3 days
28. 28.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹200 (c) ₹240 (d) ₹40
29. 29.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 23 days (c) 8 days (d) 22 days
30. 30.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹220 (c) ₹44 (d) ₹176
31. 31.₹360 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹360 (b) ₹180 (c) ₹315 (d) ₹45
32. 32.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹40 (b) ₹21 (c) ₹60 (d) ₹30
33. 33.₹224 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹32 (b) ₹96 (c) ₹112 (d) ₹128
34. 34.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
35. 35.If 9 mangoes cost ₹135, how much do 2 mangoes cost? (a) ₹270 (b) ₹45 (c) ₹30 (d) ₹128
36. 36.If 8 notebooks cost ₹184, how much do 2 notebooks cost? (a) ₹69 (b) ₹368 (c) ₹178 (d) ₹46
37. 37.If 3 kites cost ₹39, how much do 12 kites cost? (a) ₹468 (b) ₹156 (c) ₹169 (d) ₹48
38. 38.If 3 pens cost ₹39, how much do 2 pens cost? (a) ₹39 (b) ₹38 (c) ₹78 (d) ₹26
39. 39.If 8 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹70 (b) ₹63 (c) ₹57 (d) ₹504
40. 40.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 3 days (d) 2 days

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