Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 398 · 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.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹144 (b) ₹72 (c) ₹126 (d) ₹18
2. 2.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹50 (c) ₹40 (d) ₹60
3. 3.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 9 days (d) 4 days
4. 4.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 18 days (d) 15 days
5. 5.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹35 (c) ₹5 (d) ₹25
6. 6.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹336 (d) ₹432
7. 7.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
8. 8.If 4 kites cost ₹28, how much do 5 kites cost? (a) ₹42 (b) ₹140 (c) ₹29 (d) ₹35
9. 9.If 7 pens cost ₹119, how much do 11 pens cost? (a) ₹204 (b) ₹1309 (c) ₹123 (d) ₹187
10. 10.If 5 mangoes cost ₹80, how much do 6 mangoes cost? (a) ₹81 (b) ₹96 (c) ₹112 (d) ₹480
11. 11.If 4 kites cost ₹28, how much do 9 kites cost? (a) ₹70 (b) ₹33 (c) ₹63 (d) ₹252
12. 12.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹195 (d) ₹234
13. 13.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 10 days (d) 9 days
14. 14.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 13 days (d) 21 days
15. 15.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹266 (b) ₹152 (c) ₹38 (d) ₹304
16. 16.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 2 days (d) 3 days
17. 17.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹39 (b) ₹312 (c) ₹156 (d) ₹273
18. 18.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 2 days
19. 19.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 11 days
20. 20.If 6 mangoes cost ₹150, how much do 5 mangoes cost? (a) ₹125 (b) ₹150 (c) ₹750 (d) ₹149
21. 21.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 8 days (d) 18 days
22. 22.If 4 pens cost ₹80, how much do 10 pens cost? (a) ₹220 (b) ₹800 (c) ₹200 (d) ₹86
23. 23.If 6 notebooks cost ₹144, how much do 9 notebooks cost? (a) ₹1296 (b) ₹147 (c) ₹240 (d) ₹216
24. 24.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 22 days (d) 23 days
25. 25.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹129 (b) ₹87 (c) ₹86 (d) ₹43
26. 26.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 15 days
27. 27.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 14 days (d) 6 days
28. 28.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹7 (b) ₹57 (c) ₹63 (d) ₹56
29. 29.If 2 kites cost ₹30, how much do 6 kites cost? (a) ₹34 (b) ₹90 (c) ₹180 (d) ₹105
30. 30.If 3 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹35 (b) ₹72 (c) ₹36 (d) ₹24
31. 31.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 14 days (d) 11 days
32. 32.If 2 kites cost ₹48, how much do 6 kites cost? (a) ₹52 (b) ₹288 (c) ₹168 (d) ₹144
33. 33.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹55 (b) ₹33 (c) ₹77 (d) ₹11
34. 34.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹225 (b) ₹270 (c) ₹45 (d) ₹315
35. 35.If 7 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹210 (b) ₹33 (c) ₹24 (d) ₹30
36. 36.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 6 days (d) 36 days
37. 37.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 11 days (d) 7 days
38. 38.If 4 mangoes cost ₹44, how much do 7 mangoes cost? (a) ₹308 (b) ₹47 (c) ₹77 (d) ₹88
39. 39.₹396 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹198 (b) ₹252 (c) ₹36 (d) ₹144
40. 40.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 41 days (d) 40 days

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