Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 590 · 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. 1.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 15 days (d) 13 days
2. 2.If 8 kites cost ₹112, how much do 12 kites cost? (a) ₹1344 (b) ₹182 (c) ₹168 (d) ₹116
3. 3.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 3 days (d) 12 days
4. 4.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹329 (b) ₹282 (c) ₹47 (d) ₹235
5. 5.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹432 (b) ₹312 (c) ₹48 (d) ₹192
6. 6.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 15 days (c) 9 days (d) 16 days
7. 7.If 2 pens cost ₹16, how much do 10 pens cost? (a) ₹24 (b) ₹80 (c) ₹160 (d) ₹88
8. 8.If 7 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹504 (b) ₹81 (c) ₹72 (d) ₹64
9. 9.₹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
10. 10.₹154 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹77 (b) ₹110 (c) ₹44 (d) ₹22
11. 11.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹215 (b) ₹172 (c) ₹43 (d) ₹129
12. 12.If 3 pens cost ₹42, how much do 2 pens cost? (a) ₹42 (b) ₹28 (c) ₹84 (d) ₹41
13. 13.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹85 (b) ₹119 (c) ₹102 (d) ₹17
14. 14.If 9 pens cost ₹126, how much do 10 pens cost? (a) ₹154 (b) ₹127 (c) ₹1260 (d) ₹140
15. 15.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 1 day
16. 16.If 9 notebooks cost ₹216, how much do 11 notebooks cost? (a) ₹288 (b) ₹2376 (c) ₹264 (d) ₹218
17. 17.If 2 mangoes cost ₹24, how much do 8 mangoes cost? (a) ₹30 (b) ₹96 (c) ₹192 (d) ₹108
18. 18.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 25 days (d) 9 days
19. 19.If 3 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹28 (b) ₹22 (c) ₹35 (d) ₹84
20. 20.If 5 pens cost ₹30, how much do 4 pens cost? (a) ₹29 (b) ₹120 (c) ₹30 (d) ₹24
21. 21.If 3 kites cost ₹15, how much do 2 kites cost? (a) ₹10 (b) ₹14 (c) ₹30 (d) ₹15
22. 22.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹48 (c) ₹192 (d) ₹240
23. 23.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹13 (b) ₹117 (c) ₹52 (d) ₹130
24. 24.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 22 days (c) 15 days (d) 23 days
25. 25.If 7 mangoes cost ₹56, how much do 12 mangoes cost? (a) ₹61 (b) ₹104 (c) ₹672 (d) ₹96
26. 26.If 5 notebooks cost ₹105, how much do 8 notebooks cost? (a) ₹840 (b) ₹189 (c) ₹168 (d) ₹108
27. 27.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 15 days (d) 11 days
28. 28.If 8 pens cost ₹88, how much do 2 pens cost? (a) ₹176 (b) ₹22 (c) ₹33 (d) ₹82
29. 29.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 13 days (d) 28 days
30. 30.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 13 days (d) 9 days
31. 31.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 8 days (d) 10 days
32. 32.If 2 kites cost ₹46, how much do 10 kites cost? (a) ₹460 (b) ₹253 (c) ₹54 (d) ₹230
33. 33.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 35 days (c) 36 days (d) 5 days
34. 34.If 6 pens cost ₹48, how much do 11 pens cost? (a) ₹53 (b) ₹96 (c) ₹88 (d) ₹528
35. 35.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹36 (d) ₹72
36. 36.If 4 notebooks cost ₹20, how much do 7 notebooks cost? (a) ₹40 (b) ₹35 (c) ₹140 (d) ₹23
37. 37.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 5 days (d) 44 days
38. 38.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹264 (b) ₹44 (c) ₹220 (d) ₹242
39. 39.₹36 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹36 (b) ₹6 (c) ₹18 (d) ₹30
40. 40.If 8 notebooks cost ₹48, how much do 10 notebooks cost? (a) ₹60 (b) ₹480 (c) ₹50 (d) ₹66

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