Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 917 · 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.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹245 (b) ₹210 (c) ₹35 (d) ₹175
2. 2.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 3 days
3. 3.If 4 mangoes cost ₹84, how much do 3 mangoes cost? (a) ₹252 (b) ₹63 (c) ₹84 (d) ₹83
4. 4.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 5 days (d) 16 days
5. 5.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 1 day (d) 9 days
6. 6.If 9 pens cost ₹54, how much do 4 pens cost? (a) ₹216 (b) ₹24 (c) ₹49 (d) ₹30
7. 7.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹25 (b) ₹100 (c) ₹250 (d) ₹225
8. 8.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹18 (b) ₹117 (c) ₹162 (d) ₹72
9. 9.If 5 pens cost ₹95, how much do 2 pens cost? (a) ₹92 (b) ₹190 (c) ₹38 (d) ₹57
10. 10.₹495 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹450 (b) ₹45 (c) ₹90 (d) ₹405
11. 11.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 29 days (c) 28 days (d) 13 days
12. 12.If 4 pens cost ₹16, how much do 3 pens cost? (a) ₹48 (b) ₹16 (c) ₹15 (d) ₹12
13. 13.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 11 days (d) 19 days
14. 14.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 25 days (d) 23 days
15. 15.If 2 pens cost ₹28, how much do 12 pens cost? (a) ₹168 (b) ₹38 (c) ₹336 (d) ₹182
16. 16.If 2 pens cost ₹32, how much do 11 pens cost? (a) ₹176 (b) ₹41 (c) ₹192 (d) ₹352
17. 17.If 9 kites cost ₹54, how much do 7 kites cost? (a) ₹48 (b) ₹378 (c) ₹52 (d) ₹42
18. 18.₹528 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹48 (b) ₹192 (c) ₹336 (d) ₹264
19. 19.If 2 kites cost ₹38, how much do 9 kites cost? (a) ₹45 (b) ₹342 (c) ₹171 (d) ₹190
20. 20.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 9 days (d) 19 days
21. 21.If 9 notebooks cost ₹27, how much do 5 notebooks cost? (a) ₹23 (b) ₹135 (c) ₹15 (d) ₹18
22. 22.If 7 pens cost ₹56, how much do 5 pens cost? (a) ₹54 (b) ₹40 (c) ₹280 (d) ₹48
23. 23.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 4 days (d) 3 days
24. 24.If 8 kites cost ₹128, how much do 9 kites cost? (a) ₹144 (b) ₹1152 (c) ₹129 (d) ₹160
25. 25.If 8 mangoes cost ₹24, how much do 2 mangoes cost? (a) ₹18 (b) ₹9 (c) ₹48 (d) ₹6
26. 26.If 5 kites cost ₹25, how much do 7 kites cost? (a) ₹27 (b) ₹35 (c) ₹175 (d) ₹40
27. 27.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 8 days
28. 28.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 23 days (d) 7 days
29. 29.If 6 notebooks cost ₹102, how much do 7 notebooks cost? (a) ₹714 (b) ₹136 (c) ₹103 (d) ₹119
30. 30.If 7 pens cost ₹35, how much do 9 pens cost? (a) ₹37 (b) ₹45 (c) ₹315 (d) ₹50
31. 31.₹207 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹207 (d) ₹185
32. 32.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹60 (b) ₹96 (c) ₹120 (d) ₹24
33. 33.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹72 (c) ₹24 (d) ₹120
34. 34.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 4 days (d) 5 days
35. 35.If 5 mangoes cost ₹30, how much do 11 mangoes cost? (a) ₹72 (b) ₹330 (c) ₹36 (d) ₹66
36. 36.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 4 days (d) 5 days
37. 37.If 5 kites cost ₹30, how much do 9 kites cost? (a) ₹270 (b) ₹60 (c) ₹54 (d) ₹34
38. 38.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹75 (b) ₹50 (c) ₹100 (d) ₹25
39. 39.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹175 (d) ₹150
40. 40.If 3 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹28 (b) ₹22 (c) ₹84 (d) ₹35

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