Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 526 · 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. 1.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 16 days (c) 27 days (d) 10 days
2. 2.If 9 notebooks cost ₹135, how much do 10 notebooks cost? (a) ₹136 (b) ₹1350 (c) ₹165 (d) ₹150
3. 3.If 5 pens cost ₹70, how much do 10 pens cost? (a) ₹75 (b) ₹154 (c) ₹700 (d) ₹140
4. 4.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹63 (b) ₹84 (c) ₹105 (d) ₹21
5. 5.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 5 days (d) 21 days
6. 6.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 17 days
7. 7.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
8. 8.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹27 (d) ₹81
9. 9.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹186 (b) ₹217 (c) ₹31 (d) ₹155
10. 10.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 6 days
11. 11.If 8 mangoes cost ₹200, how much do 9 mangoes cost? (a) ₹250 (b) ₹201 (c) ₹1800 (d) ₹225
12. 12.If 4 pens cost ₹20, how much do 10 pens cost? (a) ₹50 (b) ₹200 (c) ₹55 (d) ₹26
13. 13.₹360 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹36 (b) ₹108 (c) ₹252 (d) ₹180
14. 14.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 28 days (d) 10 days
15. 15.If 3 pens cost ₹27, how much do 6 pens cost? (a) ₹162 (b) ₹30 (c) ₹63 (d) ₹54
16. 16.If 5 pens cost ₹50, how much do 2 pens cost? (a) ₹47 (b) ₹30 (c) ₹20 (d) ₹100
17. 17.4 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
18. 18.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹21 (b) ₹84 (c) ₹210 (d) ₹189
19. 19.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹25 (d) ₹45
20. 20.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 21 days (d) 45 days
21. 21.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹273 (c) ₹234 (d) ₹39
22. 22.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 9 days (d) 16 days
23. 23.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹94 (b) ₹141 (c) ₹188 (d) ₹47
24. 24.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 16 days (d) 3 days
25. 25.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 27 days (d) 3 days
26. 26.If 2 pens cost ₹16, how much do 10 pens cost? (a) ₹24 (b) ₹80 (c) ₹88 (d) ₹160
27. 27.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 29 days (d) 28 days
28. 28.If 6 notebooks cost ₹126, how much do 5 notebooks cost? (a) ₹125 (b) ₹126 (c) ₹105 (d) ₹630
29. 29.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 7 days (d) 39 days
30. 30.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 16 days (d) 1 day
31. 31.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹207 (b) ₹69 (c) ₹23 (d) ₹184
32. 32.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 6 days (d) 14 days
33. 33.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 5 days (d) 15 days
34. 34.If 2 mangoes cost ₹38, how much do 7 mangoes cost? (a) ₹266 (b) ₹133 (c) ₹152 (d) ₹43
35. 35.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 10 days (d) 7 days
36. 36.9 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) 21 days (d) 13 days
37. 37.If 4 notebooks cost ₹88, how much do 6 notebooks cost? (a) ₹154 (b) ₹90 (c) ₹528 (d) ₹132
38. 38.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹238 (b) ₹272 (c) ₹34 (d) ₹136
39. 39.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹174 (b) ₹116 (c) ₹29 (d) ₹145
40. 40.If 7 kites cost ₹21, how much do 12 kites cost? (a) ₹36 (b) ₹26 (c) ₹252 (d) ₹39

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