Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 359 · 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 6 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 11 days (d) 21 days
2. 2.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 17 days (d) 10 days
3. 3.If 4 kites cost ₹92, how much do 5 kites cost? (a) ₹93 (b) ₹138 (c) ₹115 (d) ₹460
4. 4.If 4 kites cost ₹52, how much do 7 kites cost? (a) ₹364 (b) ₹55 (c) ₹104 (d) ₹91
5. 5.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹300 (b) ₹275 (c) ₹50 (d) ₹250
6. 6.If 9 kites cost ₹117, how much do 12 kites cost? (a) ₹156 (b) ₹1404 (c) ₹169 (d) ₹120
7. 7.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹430 (b) ₹215 (c) ₹43 (d) ₹387
8. 8.If 3 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹75 (b) ₹60 (c) ₹180 (d) ₹46
9. 9.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
10. 10.If 7 mangoes cost ₹63, how much do 2 mangoes cost? (a) ₹126 (b) ₹58 (c) ₹18 (d) ₹27
11. 11.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹119 (b) ₹102 (c) ₹17 (d) ₹85
12. 12.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 16 days (d) 13 days
13. 13.If 6 pens cost ₹90, how much do 7 pens cost? (a) ₹630 (b) ₹91 (c) ₹120 (d) ₹105
14. 14.If 8 notebooks cost ₹136, how much do 4 notebooks cost? (a) ₹68 (b) ₹85 (c) ₹544 (d) ₹132
15. 15.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 27 days (d) 7 days
16. 16.If 3 pens cost ₹69, how much do 10 pens cost? (a) ₹230 (b) ₹253 (c) ₹76 (d) ₹690
17. 17.If 5 notebooks cost ₹90, how much do 3 notebooks cost? (a) ₹72 (b) ₹270 (c) ₹54 (d) ₹88
18. 18.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹30 (b) ₹15 (c) ₹135 (d) ₹150
19. 19.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹20 (b) ₹180 (c) ₹110 (d) ₹40
20. 20.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹192 (c) ₹24 (d) ₹72
21. 21.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹56 (b) ₹80 (c) ₹32 (d) ₹16
22. 22.If 6 pens cost ₹72, how much do 10 pens cost? (a) ₹76 (b) ₹720 (c) ₹120 (d) ₹132
23. 23.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹92 (b) ₹230 (c) ₹23 (d) ₹207
24. 24.If 3 kites cost ₹75, how much do 4 kites cost? (a) ₹76 (b) ₹100 (c) ₹125 (d) ₹300
25. 25.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 14 days (d) 11 days
26. 26.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 19 days (d) 7 days
27. 27.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹92 (d) ₹69
28. 28.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 7 days (c) 17 days (d) 43 days
29. 29.If 3 kites cost ₹39, how much do 10 kites cost? (a) ₹390 (b) ₹130 (c) ₹143 (d) ₹46
30. 30.If 7 pens cost ₹133, how much do 4 pens cost? (a) ₹95 (b) ₹130 (c) ₹532 (d) ₹76
31. 31.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹10 (c) ₹25 (d) ₹20
32. 32.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹121 (b) ₹44 (c) ₹22 (d) ₹198
33. 33.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹70 (b) ₹7 (c) ₹28 (d) ₹63
34. 34.If 9 notebooks cost ₹189, how much do 7 notebooks cost? (a) ₹168 (b) ₹147 (c) ₹187 (d) ₹1323
35. 35.If 8 mangoes cost ₹72, how much do 3 mangoes cost? (a) ₹67 (b) ₹36 (c) ₹216 (d) ₹27
36. 36.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 21 days (b) 48 days (c) 4 days (d) 3 days
37. 37.If 9 kites cost ₹54, how much do 10 kites cost? (a) ₹60 (b) ₹66 (c) ₹55 (d) ₹540
38. 38.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 4 days (d) 3 days
39. 39.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
40. 40.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 1 day (d) 8 days

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