Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 154 · 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.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹224 (d) ₹288
2. 2.If 7 notebooks cost ₹175, how much do 9 notebooks cost? (a) ₹250 (b) ₹177 (c) ₹225 (d) ₹1575
3. 3.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 5 days (d) 3 days
4. 4.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 9 days (d) 8 days
5. 5.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹38 (b) ₹190 (c) ₹171 (d) ₹19
6. 6.If 9 pens cost ₹153, how much do 3 pens cost? (a) ₹459 (b) ₹147 (c) ₹68 (d) ₹51
7. 7.4 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
8. 8.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹38 (b) ₹152 (c) ₹209 (d) ₹266
9. 9.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹120 (b) ₹15 (c) ₹135 (d) ₹121
10. 10.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 13 days (d) 20 days
11. 11.If 4 notebooks cost ₹88, how much do 11 notebooks cost? (a) ₹95 (b) ₹242 (c) ₹264 (d) ₹968
12. 12.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 28 days (b) 19 days (c) 7 days (d) 9 days
13. 13.If 4 pens cost ₹40, how much do 10 pens cost? (a) ₹100 (b) ₹110 (c) ₹400 (d) ₹46
14. 14.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 17 days (c) 7 days (d) 33 days
15. 15.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹54 (b) ₹36 (c) ₹18 (d) ₹45
16. 16.If 8 pens cost ₹160, how much do 4 pens cost? (a) ₹156 (b) ₹80 (c) ₹640 (d) ₹100
17. 17.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹184 (d) ₹138
18. 18.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹266 (b) ₹38 (c) ₹152 (d) ₹304
19. 19.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹27 (b) ₹24 (c) ₹22 (d) ₹168
20. 20.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹114 (b) ₹57 (c) ₹76 (d) ₹38
21. 21.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 27 days (d) 15 days
22. 22.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 7 days
23. 23.If 8 mangoes cost ₹160, how much do 11 mangoes cost? (a) ₹220 (b) ₹1760 (c) ₹240 (d) ₹163
24. 24.If 9 kites cost ₹45, how much do 8 kites cost? (a) ₹360 (b) ₹45 (c) ₹40 (d) ₹44
25. 25.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹225 (b) ₹45 (c) ₹270 (d) ₹90
26. 26.If 7 pens cost ₹119, how much do 5 pens cost? (a) ₹117 (b) ₹595 (c) ₹102 (d) ₹85
27. 27.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹55 (d) ₹45
28. 28.If 5 mangoes cost ₹125, how much do 7 mangoes cost? (a) ₹127 (b) ₹200 (c) ₹875 (d) ₹175
29. 29.If 7 notebooks cost ₹42, how much do 2 notebooks cost? (a) ₹12 (b) ₹84 (c) ₹37 (d) ₹18
30. 30.If 9 mangoes cost ₹45, how much do 5 mangoes cost? (a) ₹225 (b) ₹30 (c) ₹25 (d) ₹41
31. 31.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 8 days (d) 6 days
32. 32.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 3 days (d) 4 days
33. 33.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 18 days (d) 19 days
34. 34.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 34 days (c) 17 days (d) 33 days
35. 35.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 2 days (d) 7 days
36. 36.If 3 kites cost ₹48, how much do 6 kites cost? (a) ₹112 (b) ₹96 (c) ₹288 (d) ₹51
37. 37.If 9 pens cost ₹198, how much do 12 pens cost? (a) ₹286 (b) ₹201 (c) ₹2376 (d) ₹264
38. 38.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 53 days (c) 19 days (d) 52 days
39. 39.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
40. 40.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹378 (b) ₹210 (c) ₹42 (d) ₹294

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