Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 447 · 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.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹329 (b) ₹141 (c) ₹235 (d) ₹47
2. 2.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 5 days (d) 13 days
3. 3.7 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) 8 days (d) 6 days
4. 4.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹27 (c) ₹45 (d) ₹9
5. 5.If 5 kites cost ₹80, how much do 12 kites cost? (a) ₹192 (b) ₹87 (c) ₹960 (d) ₹208
6. 6.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 5 days (d) 14 days
7. 7.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹115 (d) ₹69
8. 8.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 5 days (d) 7 days
9. 9.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 11 days (d) 6 days
10. 10.If 3 kites cost ₹39, how much do 10 kites cost? (a) ₹130 (b) ₹143 (c) ₹46 (d) ₹390
11. 11.5 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
12. 12.If 5 mangoes cost ₹55, how much do 6 mangoes cost? (a) ₹77 (b) ₹66 (c) ₹330 (d) ₹56
13. 13.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
14. 14.6 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) 5 days (d) 6 days
15. 15.If 6 kites cost ₹126, how much do 11 kites cost? (a) ₹231 (b) ₹1386 (c) ₹252 (d) ₹131
16. 16.If 5 kites cost ₹25, how much do 8 kites cost? (a) ₹28 (b) ₹40 (c) ₹200 (d) ₹45
17. 17.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 5 days (d) 7 days
18. 18.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹225 (b) ₹250 (c) ₹25 (d) ₹100
19. 19.If 7 mangoes cost ₹56, how much do 4 mangoes cost? (a) ₹53 (b) ₹224 (c) ₹40 (d) ₹32
20. 20.If 4 mangoes cost ₹16, how much do 9 mangoes cost? (a) ₹40 (b) ₹36 (c) ₹21 (d) ₹144
21. 21.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 18 days (d) 19 days
22. 22.If 5 kites cost ₹45, how much do 3 kites cost? (a) ₹27 (b) ₹135 (c) ₹43 (d) ₹36
23. 23.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 4 days (d) 3 days
24. 24.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 3 days (d) 11 days
25. 25.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹182 (b) ₹78 (c) ₹130 (d) ₹26
26. 26.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 2 days (d) 32 days
27. 27.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 19 days (d) 28 days
28. 28.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹165 (d) ₹231
29. 29.If 2 notebooks cost ₹18, how much do 11 notebooks cost? (a) ₹198 (b) ₹99 (c) ₹27 (d) ₹108
30. 30.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹10 (c) ₹20 (d) ₹30
31. 31.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹78 (d) ₹13
32. 32.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 12 days
33. 33.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹96 (b) ₹240 (c) ₹168 (d) ₹48
34. 34.If 7 pens cost ₹147, how much do 2 pens cost? (a) ₹42 (b) ₹294 (c) ₹142 (d) ₹63
35. 35.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹111 (d) ₹74
36. 36.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹121 (b) ₹66 (c) ₹22 (d) ₹176
37. 37.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 14 days
38. 38.If 8 mangoes cost ₹192, how much do 7 mangoes cost? (a) ₹1344 (b) ₹168 (c) ₹192 (d) ₹191
39. 39.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 30 days (c) 13 days (d) 31 days
40. 40.If 3 kites cost ₹63, how much do 5 kites cost? (a) ₹105 (b) ₹315 (c) ₹126 (d) ₹65

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