Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 251 · 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. 1.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 11 days (d) 8 days
2. 2.If 8 pens cost ₹152, how much do 3 pens cost? (a) ₹456 (b) ₹147 (c) ₹57 (d) ₹76
3. 3.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹115 (b) ₹207 (c) ₹161 (d) ₹23
4. 4.If 7 pens cost ₹70, how much do 2 pens cost? (a) ₹140 (b) ₹20 (c) ₹30 (d) ₹65
5. 5.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 7 days (d) 13 days
6. 6.If 5 pens cost ₹100, how much do 2 pens cost? (a) ₹60 (b) ₹97 (c) ₹40 (d) ₹200
7. 7.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 4 days (d) 36 days
8. 8.If 4 mangoes cost ₹68, how much do 6 mangoes cost? (a) ₹102 (b) ₹119 (c) ₹408 (d) ₹70
9. 9.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 15 days
10. 10.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 13 days (d) 9 days
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) 1 day (c) 7 days (d) 2 days
12. 12.If 3 mangoes cost ₹36, how much do 2 mangoes cost? (a) ₹35 (b) ₹36 (c) ₹24 (d) ₹72
13. 13.If 7 notebooks cost ₹84, how much do 12 notebooks cost? (a) ₹89 (b) ₹144 (c) ₹156 (d) ₹1008
14. 14.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 49 days (d) 4 days
15. 15.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹110 (b) ₹120 (c) ₹100 (d) ₹20
16. 16.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 9 days (d) 2 days
17. 17.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹31 (d) ₹45
18. 18.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 19 days (d) 27 days
19. 19.₹224 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹84 (b) ₹112 (c) ₹28 (d) ₹140
20. 20.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 6 days (d) 3 days
21. 21.If 3 kites cost ₹48, how much do 10 kites cost? (a) ₹55 (b) ₹176 (c) ₹480 (d) ₹160
22. 22.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 9 days (d) 13 days
23. 23.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 30 days (c) 11 days (d) 31 days
24. 24.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹160 (b) ₹128 (c) ₹96 (d) ₹32
25. 25.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹252 (d) ₹231
26. 26.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 17 days (d) 9 days
27. 27.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 36 days (d) 35 days
28. 28.If 4 notebooks cost ₹20, how much do 8 notebooks cost? (a) ₹40 (b) ₹24 (c) ₹160 (d) ₹45
29. 29.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹32 (b) ₹88 (c) ₹16 (d) ₹144
30. 30.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹40 (b) ₹280 (c) ₹140 (d) ₹240
31. 31.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 16 days (d) 13 days
32. 32.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 16 days (d) 17 days
33. 33.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹39 (d) ₹13
34. 34.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 7 days (d) 10 days
35. 35.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹205 (b) ₹123 (c) ₹41 (d) ₹287
36. 36.If 4 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹66 (b) ₹220 (c) ₹55 (d) ₹45
37. 37.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹51 (b) ₹102 (c) ₹17 (d) ₹85
38. 38.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 31 days (c) 30 days (d) 6 days
39. 39.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹35 (c) ₹7 (d) ₹49
40. 40.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 2 days

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