Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 197 · 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.If 6 pens cost ₹42, how much do 10 pens cost? (a) ₹46 (b) ₹77 (c) ₹420 (d) ₹70
2. 2.If 9 kites cost ₹63, how much do 4 kites cost? (a) ₹35 (b) ₹252 (c) ₹28 (d) ₹58
3. 3.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹54 (b) ₹36 (c) ₹9 (d) ₹45
4. 4.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 19 days (d) 16 days
5. 5.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
6. 6.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹154 (d) ₹88
7. 7.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹140 (b) ₹160 (c) ₹120 (d) ₹40
8. 8.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
9. 9.₹320 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹120 (c) ₹200 (d) ₹160
10. 10.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 2 days
11. 11.If 4 mangoes cost ₹52, how much do 9 mangoes cost? (a) ₹468 (b) ₹130 (c) ₹117 (d) ₹57
12. 12.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹376 (b) ₹94 (c) ₹47 (d) ₹329
13. 13.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹264 (b) ₹432 (c) ₹96 (d) ₹48
14. 14.If 2 mangoes cost ₹38, how much do 10 mangoes cost? (a) ₹46 (b) ₹190 (c) ₹380 (d) ₹209
15. 15.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 18 days (d) 2 days
16. 16.If 5 notebooks cost ₹70, how much do 8 notebooks cost? (a) ₹112 (b) ₹73 (c) ₹560 (d) ₹126
17. 17.If 6 notebooks cost ₹102, how much do 4 notebooks cost? (a) ₹408 (b) ₹100 (c) ₹85 (d) ₹68
18. 18.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹231 (b) ₹126 (c) ₹42 (d) ₹336
19. 19.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 9 days (d) 8 days
20. 20.If 5 pens cost ₹105, how much do 10 pens cost? (a) ₹110 (b) ₹210 (c) ₹231 (d) ₹1050
21. 21.If 5 kites cost ₹30, how much do 6 kites cost? (a) ₹42 (b) ₹36 (c) ₹180 (d) ₹31
22. 22.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 17 days (d) 11 days
23. 23.4 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) 10 days (d) 28 days
24. 24.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 7 days
25. 25.If 7 mangoes cost ₹49, how much do 4 mangoes cost? (a) ₹46 (b) ₹196 (c) ₹28 (d) ₹35
26. 26.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 33 days (c) 7 days (d) 15 days
27. 27.If 9 mangoes cost ₹99, how much do 4 mangoes cost? (a) ₹94 (b) ₹55 (c) ₹396 (d) ₹44
28. 28.If 4 kites cost ₹44, how much do 11 kites cost? (a) ₹132 (b) ₹484 (c) ₹51 (d) ₹121
29. 29.If 7 kites cost ₹154, how much do 9 kites cost? (a) ₹1386 (b) ₹220 (c) ₹198 (d) ₹156
30. 30.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 20 days (d) 56 days
31. 31.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 12 days
32. 32.If 3 pens cost ₹63, how much do 7 pens cost? (a) ₹67 (b) ₹441 (c) ₹147 (d) ₹168
33. 33.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹352 (c) ₹176 (d) ₹308
34. 34.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹121 (b) ₹176 (c) ₹22 (d) ₹66
35. 35.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹344 (d) ₹215
36. 36.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹105 (d) ₹15
37. 37.₹77 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹11 (d) ₹55
38. 38.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 12 days (c) 25 days (d) 24 days
39. 39.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹21 (d) ₹35
40. 40.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 39 days (d) 19 days

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