Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 791 · 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 9 pens cost ₹36, how much do 6 pens cost? (a) ₹216 (b) ₹33 (c) ₹28 (d) ₹24
2. 2.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹432 (d) ₹336
3. 3.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹38 (b) ₹190 (c) ₹342 (d) ₹380
4. 4.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 9 days (c) 27 days (d) 17 days
5. 5.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 22 days (d) 21 days
6. 6.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹12 (b) ₹72 (c) ₹84 (d) ₹60
7. 7.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 1 day (d) 6 days
8. 8.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
9. 9.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹36 (b) ₹252 (c) ₹180 (d) ₹324
10. 10.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
11. 11.If 7 pens cost ₹133, how much do 8 pens cost? (a) ₹1064 (b) ₹134 (c) ₹171 (d) ₹152
12. 12.If 5 pens cost ₹105, how much do 12 pens cost? (a) ₹112 (b) ₹252 (c) ₹1260 (d) ₹273
13. 13.If 2 kites cost ₹28, how much do 5 kites cost? (a) ₹31 (b) ₹84 (c) ₹70 (d) ₹140
14. 14.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹132 (d) ₹165
15. 15.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹138 (b) ₹230 (c) ₹46 (d) ₹184
16. 16.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 11 days (d) 16 days
17. 17.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 18 days (d) 12 days
18. 18.If 9 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹18 (b) ₹12 (c) ₹47 (d) ₹108
19. 19.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 5 days (d) 3 days
20. 20.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹72 (b) ₹18 (c) ₹90 (d) ₹81
21. 21.If 8 pens cost ₹80, how much do 9 pens cost? (a) ₹90 (b) ₹720 (c) ₹100 (d) ₹81
22. 22.If 6 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹240 (b) ₹50 (c) ₹58 (d) ₹40
23. 23.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 13 days (c) 31 days (d) 17 days
24. 24.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹33 (b) ₹77 (c) ₹55 (d) ₹11
25. 25.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹36 (c) ₹9 (d) ₹54
26. 26.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹55 (b) ₹10 (c) ₹80 (d) ₹30
27. 27.If 2 notebooks cost ₹30, how much do 8 notebooks cost? (a) ₹120 (b) ₹135 (c) ₹240 (d) ₹36
28. 28.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹312 (b) ₹48 (c) ₹384 (d) ₹240
29. 29.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 4 days (d) 5 days
30. 30.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹82 (b) ₹164 (c) ₹41 (d) ₹123
31. 31.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 23 days (c) 5 days (d) 45 days
32. 32.If 2 notebooks cost ₹40, how much do 8 notebooks cost? (a) ₹160 (b) ₹180 (c) ₹320 (d) ₹46
33. 33.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹88 (b) ₹198 (c) ₹44 (d) ₹308
34. 34.If 7 notebooks cost ₹168, how much do 8 notebooks cost? (a) ₹216 (b) ₹1344 (c) ₹192 (d) ₹169
35. 35.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹44 (c) ₹352 (d) ₹242
36. 36.If 9 notebooks cost ₹162, how much do 8 notebooks cost? (a) ₹144 (b) ₹1296 (c) ₹161 (d) ₹162
37. 37.If 6 pens cost ₹126, how much do 7 pens cost? (a) ₹127 (b) ₹882 (c) ₹147 (d) ₹168
38. 38.If 2 mangoes cost ₹18, how much do 6 mangoes cost? (a) ₹22 (b) ₹63 (c) ₹108 (d) ₹54
39. 39.If 6 notebooks cost ₹42, how much do 2 notebooks cost? (a) ₹38 (b) ₹21 (c) ₹84 (d) ₹14
40. 40.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹29 (b) ₹290 (c) ₹261 (d) ₹116

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