Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 57 · 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. 1.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 37 days (d) 1 day
2. 2.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 17 days
3. 3.If 7 notebooks cost ₹56, how much do 10 notebooks cost? (a) ₹560 (b) ₹59 (c) ₹80 (d) ₹88
4. 4.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹155 (d) ₹279
5. 5.If 5 kites cost ₹60, how much do 2 kites cost? (a) ₹36 (b) ₹24 (c) ₹57 (d) ₹120
6. 6.If 9 pens cost ₹81, how much do 7 pens cost? (a) ₹72 (b) ₹79 (c) ₹63 (d) ₹567
7. 7.If 7 mangoes cost ₹105, how much do 12 mangoes cost? (a) ₹110 (b) ₹1260 (c) ₹195 (d) ₹180
8. 8.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹81 (b) ₹90 (c) ₹18 (d) ₹72
9. 9.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹54 (b) ₹63 (c) ₹45 (d) ₹9
10. 10.If 3 mangoes cost ₹27, how much do 11 mangoes cost? (a) ₹108 (b) ₹297 (c) ₹35 (d) ₹99
11. 11.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹160 (b) ₹128 (c) ₹32 (d) ₹144
12. 12.If 8 notebooks cost ₹144, how much do 12 notebooks cost? (a) ₹1728 (b) ₹216 (c) ₹234 (d) ₹148
13. 13.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 28 days (d) 18 days
14. 14.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹48 (d) ₹72
15. 15.If 3 notebooks cost ₹54, how much do 5 notebooks cost? (a) ₹90 (b) ₹108 (c) ₹270 (d) ₹56
16. 16.₹405 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹270 (b) ₹225 (c) ₹45 (d) ₹180
17. 17.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹16 (c) ₹20 (d) ₹24
18. 18.If 6 mangoes cost ₹120, how much do 4 mangoes cost? (a) ₹480 (b) ₹118 (c) ₹80 (d) ₹100
19. 19.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹301 (b) ₹215 (c) ₹43 (d) ₹258
20. 20.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 13 days (d) 5 days
21. 21.If 7 pens cost ₹168, how much do 8 pens cost? (a) ₹216 (b) ₹169 (c) ₹1344 (d) ₹192
22. 22.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 28 days (d) 3 days
23. 23.If 2 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹72 (b) ₹36 (c) ₹45 (d) ₹20
24. 24.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹6 (d) ₹12
25. 25.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹65 (b) ₹91 (c) ₹13 (d) ₹39
26. 26.If 3 pens cost ₹42, how much do 7 pens cost? (a) ₹294 (b) ₹46 (c) ₹98 (d) ₹112
27. 27.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 5 days (d) 20 days
28. 28.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹171 (d) ₹95
29. 29.If 7 kites cost ₹133, how much do 9 kites cost? (a) ₹171 (b) ₹190 (c) ₹135 (d) ₹1197
30. 30.If 3 pens cost ₹63, how much do 2 pens cost? (a) ₹63 (b) ₹126 (c) ₹42 (d) ₹62
31. 31.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 6 days (d) 4 days
32. 32.If 4 kites cost ₹24, how much do 12 kites cost? (a) ₹288 (b) ₹72 (c) ₹78 (d) ₹32
33. 33.If 2 kites cost ₹30, how much do 8 kites cost? (a) ₹135 (b) ₹120 (c) ₹36 (d) ₹240
34. 34.If 3 pens cost ₹48, how much do 4 pens cost? (a) ₹192 (b) ₹49 (c) ₹64 (d) ₹80
35. 35.If 3 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹53 (b) ₹36 (c) ₹108 (d) ₹54
36. 36.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 3 days (d) 15 days
37. 37.If 8 notebooks cost ₹176, how much do 9 notebooks cost? (a) ₹1584 (b) ₹177 (c) ₹220 (d) ₹198
38. 38.If 3 pens cost ₹57, how much do 11 pens cost? (a) ₹228 (b) ₹65 (c) ₹627 (d) ₹209
39. 39.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days
40. 40.If 6 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹420 (b) ₹70 (c) ₹84 (d) ₹83

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