Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 910 · 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.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹238 (b) ₹119 (c) ₹204 (d) ₹34
2. 2.If 8 notebooks cost ₹112, how much do 7 notebooks cost? (a) ₹784 (b) ₹112 (c) ₹98 (d) ₹111
3. 3.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹333 (b) ₹297 (c) ₹37 (d) ₹296
4. 4.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 6 days (d) 5 days
5. 5.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹68 (b) ₹119 (c) ₹17 (d) ₹136
6. 6.If 5 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹840 (b) ₹168 (c) ₹192 (d) ₹122
7. 7.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹376 (b) ₹47 (c) ₹329 (d) ₹94
8. 8.If 3 pens cost ₹45, how much do 8 pens cost? (a) ₹50 (b) ₹360 (c) ₹120 (d) ₹135
9. 9.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 2 days (d) 3 days
10. 10.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹44 (b) ₹154 (c) ₹176 (d) ₹132
11. 11.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 10 days (d) 11 days
12. 12.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 6 days
13. 13.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 7 days (d) 10 days
14. 14.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹105 (c) ₹140 (d) ₹175
15. 15.If 4 pens cost ₹48, how much do 9 pens cost? (a) ₹108 (b) ₹120 (c) ₹53 (d) ₹432
16. 16.If 7 mangoes cost ₹70, how much do 3 mangoes cost? (a) ₹40 (b) ₹30 (c) ₹210 (d) ₹66
17. 17.If 6 kites cost ₹138, how much do 7 kites cost? (a) ₹161 (b) ₹966 (c) ₹139 (d) ₹184
18. 18.If 4 pens cost ₹28, how much do 3 pens cost? (a) ₹27 (b) ₹21 (c) ₹28 (d) ₹84
19. 19.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹45 (b) ₹60 (c) ₹75 (d) ₹15
20. 20.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹62 (b) ₹217 (c) ₹31 (d) ₹248
21. 21.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 5 days (d) 33 days
22. 22.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹189 (d) ₹168
23. 23.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹129 (b) ₹43 (c) ₹87 (d) ₹86
24. 24.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 17 days
25. 25.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹31 (b) ₹63 (c) ₹93 (d) ₹62
26. 26.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 7 days
27. 27.If 4 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹84 (b) ₹280 (c) ₹70 (d) ₹57
28. 28.₹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
29. 29.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 5 days (d) 25 days
30. 30.If 2 notebooks cost ₹8, how much do 9 notebooks cost? (a) ₹36 (b) ₹72 (c) ₹15 (d) ₹40
31. 31.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹161 (b) ₹207 (c) ₹115 (d) ₹23
32. 32.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 10 days
33. 33.If 5 notebooks cost ₹85, how much do 11 notebooks cost? (a) ₹91 (b) ₹204 (c) ₹187 (d) ₹935
34. 34.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹84 (b) ₹126 (c) ₹42 (d) ₹63
35. 35.₹36 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹30 (d) ₹6
36. 36.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹48 (b) ₹288 (c) ₹336 (d) ₹240
37. 37.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
38. 38.If 5 pens cost ₹115, how much do 3 pens cost? (a) ₹345 (b) ₹92 (c) ₹113 (d) ₹69
39. 39.If 8 mangoes cost ₹80, how much do 3 mangoes cost? (a) ₹75 (b) ₹30 (c) ₹40 (d) ₹240
40. 40.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 45 days (d) 5 days

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