Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 820 · 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 2 notebooks cost ₹8, how much do 6 notebooks cost? (a) ₹12 (b) ₹24 (c) ₹48 (d) ₹28
2. 2.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 3 days
3. 3.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 7 days (d) 8 days
4. 4.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 1 day
5. 5.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 9 days (d) 8 days
6. 6.If 3 pens cost ₹63, how much do 2 pens cost? (a) ₹126 (b) ₹63 (c) ₹62 (d) ₹42
7. 7.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 15 days (d) 3 days
8. 8.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 30 days (b) 11 days (c) 31 days (d) 19 days
9. 9.If 6 pens cost ₹108, how much do 2 pens cost? (a) ₹216 (b) ₹54 (c) ₹36 (d) ₹104
10. 10.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹343 (d) ₹147
11. 11.If 5 notebooks cost ₹20, how much do 2 notebooks cost? (a) ₹40 (b) ₹17 (c) ₹12 (d) ₹8
12. 12.If 5 pens cost ₹20, how much do 2 pens cost? (a) ₹40 (b) ₹17 (c) ₹8 (d) ₹12
13. 13.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹27 (c) ₹54 (d) ₹243
14. 14.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹35 (d) ₹42
15. 15.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹66 (d) ₹72
16. 16.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 5 days (d) 3 days
17. 17.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹90 (c) ₹162 (d) ₹18
18. 18.If 2 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹54 (b) ₹150 (c) ₹300 (d) ₹175
19. 19.If 2 pens cost ₹38, how much do 7 pens cost? (a) ₹43 (b) ₹133 (c) ₹152 (d) ₹266
20. 20.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹180 (c) ₹36 (d) ₹144
21. 21.If 2 notebooks cost ₹18, how much do 8 notebooks cost? (a) ₹81 (b) ₹24 (c) ₹144 (d) ₹72
22. 22.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹93 (b) ₹124 (c) ₹31 (d) ₹155
23. 23.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹90 (d) ₹135
24. 24.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹99 (b) ₹44 (c) ₹154 (d) ₹22
25. 25.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 16 days
26. 26.If 4 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹14 (b) ₹72 (c) ₹21 (d) ₹18
27. 27.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹288 (d) ₹224
28. 28.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹80 (c) ₹10 (d) ₹65
29. 29.If 4 pens cost ₹32, how much do 11 pens cost? (a) ₹88 (b) ₹352 (c) ₹96 (d) ₹39
30. 30.If 4 pens cost ₹36, how much do 10 pens cost? (a) ₹90 (b) ₹360 (c) ₹99 (d) ₹42
31. 31.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹104 (b) ₹105 (c) ₹13 (d) ₹117
32. 32.₹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
33. 33.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹70 (c) ₹10 (d) ₹50
34. 34.If 3 mangoes cost ₹39, how much do 4 mangoes cost? (a) ₹65 (b) ₹40 (c) ₹156 (d) ₹52
35. 35.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹250 (d) ₹175
36. 36.If 8 kites cost ₹152, how much do 9 kites cost? (a) ₹171 (b) ₹190 (c) ₹1368 (d) ₹153
37. 37.If 2 notebooks cost ₹8, how much do 8 notebooks cost? (a) ₹64 (b) ₹14 (c) ₹36 (d) ₹32
38. 38.₹96 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹48 (b) ₹84 (c) ₹96 (d) ₹12
39. 39.If 6 pens cost ₹30, how much do 9 pens cost? (a) ₹50 (b) ₹45 (c) ₹270 (d) ₹33
40. 40.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 9 days (c) 13 days (d) 22 days

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