Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 21 · 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 14 days. How many days will 3 workers take, working at the same speed? (a) 42 days (b) 43 days (c) 8 days (d) 20 days
2. 2.If 4 pens cost ₹20, how much do 11 pens cost? (a) ₹220 (b) ₹27 (c) ₹60 (d) ₹55
3. 3.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 1 day (d) 11 days
4. 4.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
5. 5.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 16 days (d) 11 days
6. 6.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹104 (b) ₹80 (c) ₹16 (d) ₹128
7. 7.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹91 (b) ₹45 (c) ₹90 (d) ₹135
8. 8.If 5 mangoes cost ₹90, how much do 11 mangoes cost? (a) ₹198 (b) ₹216 (c) ₹96 (d) ₹990
9. 9.8 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) 13 days (d) 28 days
10. 10.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹7 (c) ₹35 (d) ₹14
11. 11.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 2 days (d) 1 day
12. 12.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹10 (b) ₹60 (c) ₹50 (d) ₹30
13. 13.If 4 kites cost ₹96, how much do 11 kites cost? (a) ₹1056 (b) ₹264 (c) ₹103 (d) ₹288
14. 14.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹112 (c) ₹140 (d) ₹28
15. 15.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹37 (b) ₹296 (c) ₹74 (d) ₹259
16. 16.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹74 (b) ₹370 (c) ₹37 (d) ₹333
17. 17.If 5 mangoes cost ₹125, how much do 2 mangoes cost? (a) ₹122 (b) ₹250 (c) ₹75 (d) ₹50
18. 18.If 3 mangoes cost ₹39, how much do 8 mangoes cost? (a) ₹117 (b) ₹312 (c) ₹44 (d) ₹104
19. 19.If 6 mangoes cost ₹138, how much do 11 mangoes cost? (a) ₹1518 (b) ₹253 (c) ₹276 (d) ₹143
20. 20.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 12 days (d) 5 days
21. 21.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 10 days (d) 3 days
22. 22.If 8 pens cost ₹184, how much do 11 pens cost? (a) ₹253 (b) ₹187 (c) ₹2024 (d) ₹276
23. 23.If 2 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹45 (b) ₹90 (c) ₹60 (d) ₹31
24. 24.If 3 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹96 (b) ₹88 (c) ₹264 (d) ₹32
25. 25.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
26. 26.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹18 (b) ₹63 (c) ₹126 (d) ₹108
27. 27.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹99 (b) ₹165 (c) ₹132 (d) ₹33
28. 28.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹42 (b) ₹168 (c) ₹294 (d) ₹231
29. 29.If 5 pens cost ₹65, how much do 11 pens cost? (a) ₹143 (b) ₹156 (c) ₹71 (d) ₹715
30. 30.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 35 days (d) 36 days
31. 31.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 8 days (d) 9 days
32. 32.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹75 (b) ₹105 (c) ₹135 (d) ₹15
33. 33.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 11 days (d) 8 days
34. 34.If 8 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹51 (b) ₹528 (c) ₹66 (d) ₹72
35. 35.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹315 (b) ₹135 (c) ₹45 (d) ₹225
36. 36.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 5 days (d) 6 days
37. 37.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 13 days (d) 12 days
38. 38.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 4 days (d) 2 days
39. 39.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹249 (b) ₹31 (c) ₹248 (d) ₹279
40. 40.If 2 kites cost ₹8, how much do 4 kites cost? (a) ₹20 (b) ₹10 (c) ₹16 (d) ₹32

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