Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 36 · 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 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 27 days (d) 28 days
2. 2.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 9 days (d) 12 days
3. 3.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
4. 4.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹126 (d) ₹105
5. 5.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹24 (b) ₹144 (c) ₹120 (d) ₹168
6. 6.If 2 mangoes cost ₹28, how much do 11 mangoes cost? (a) ₹168 (b) ₹154 (c) ₹37 (d) ₹308
7. 7.₹240 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹240 (b) ₹120 (c) ₹210 (d) ₹30
8. 8.₹341 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹93 (b) ₹279 (c) ₹31 (d) ₹248
9. 9.If 9 pens cost ₹171, how much do 7 pens cost? (a) ₹133 (b) ₹1197 (c) ₹152 (d) ₹169
10. 10.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹351 (c) ₹39 (d) ₹312
11. 11.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 3 days (d) 2 days
12. 12.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 40 days (d) 19 days
13. 13.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 11 days (d) 9 days
14. 14.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹264 (c) ₹132 (d) ₹231
15. 15.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 5 days (d) 22 days
16. 16.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹54 (b) ₹45 (c) ₹9 (d) ₹63
17. 17.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 10 days (c) 7 days (d) 18 days
18. 18.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹152 (b) ₹57 (c) ₹19 (d) ₹171
19. 19.If 9 kites cost ₹153, how much do 7 kites cost? (a) ₹151 (b) ₹119 (c) ₹1071 (d) ₹136
20. 20.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹55 (c) ₹44 (d) ₹11
21. 21.₹360 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹180 (b) ₹40 (c) ₹280 (d) ₹80
22. 22.If 2 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹576 (b) ₹288 (c) ₹58 (d) ₹312
23. 23.₹384 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹192 (b) ₹48 (c) ₹384 (d) ₹336
24. 24.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 11 days (d) 12 days
25. 25.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹54 (c) ₹27 (d) ₹243
26. 26.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹135 (c) ₹81 (d) ₹27
27. 27.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 14 days (c) 16 days (d) 13 days
28. 28.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹18 (d) ₹30
29. 29.If 8 kites cost ₹72, how much do 2 kites cost? (a) ₹66 (b) ₹144 (c) ₹18 (d) ₹27
30. 30.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹161 (b) ₹115 (c) ₹207 (d) ₹23
31. 31.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹225 (b) ₹315 (c) ₹270 (d) ₹45
32. 32.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 7 days (d) 20 days
33. 33.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 8 days (d) 6 days
34. 34.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹221 (b) ₹272 (c) ₹170 (d) ₹34
35. 35.₹176 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹112 (b) ₹88 (c) ₹16 (d) ₹64
36. 36.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 10 days (d) 4 days
37. 37.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 16 days (c) 4 days (d) 5 days
38. 38.If 6 pens cost ₹60, how much do 2 pens cost? (a) ₹56 (b) ₹120 (c) ₹30 (d) ₹20
39. 39.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 10 days (c) 26 days (d) 16 days
40. 40.If 7 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹280 (b) ₹44 (c) ₹40 (d) ₹31

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