Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 784 · 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. 1.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 5 days (d) 7 days
2. 2.If 9 pens cost ₹27, how much do 12 pens cost? (a) ₹39 (b) ₹30 (c) ₹324 (d) ₹36
3. 3.If 5 notebooks cost ₹110, how much do 6 notebooks cost? (a) ₹660 (b) ₹111 (c) ₹154 (d) ₹132
4. 4.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 12 days (d) 7 days
5. 5.If 6 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹40 (b) ₹360 (c) ₹66 (d) ₹60
6. 6.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹210 (b) ₹90 (c) ₹150 (d) ₹30
7. 7.If 4 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹360 (b) ₹73 (c) ₹108 (d) ₹90
8. 8.If 2 mangoes cost ₹44, how much do 3 mangoes cost? (a) ₹66 (b) ₹88 (c) ₹132 (d) ₹45
9. 9.If 7 mangoes cost ₹98, how much do 8 mangoes cost? (a) ₹112 (b) ₹126 (c) ₹99 (d) ₹784
10. 10.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 8 days (d) 6 days
11. 11.If 3 kites cost ₹39, how much do 6 kites cost? (a) ₹91 (b) ₹234 (c) ₹78 (d) ₹42
12. 12.If 2 pens cost ₹6, how much do 5 pens cost? (a) ₹18 (b) ₹9 (c) ₹30 (d) ₹15
13. 13.If 2 pens cost ₹12, how much do 4 pens cost? (a) ₹24 (b) ₹14 (c) ₹48 (d) ₹30
14. 14.If 7 pens cost ₹56, how much do 9 pens cost? (a) ₹80 (b) ₹72 (c) ₹58 (d) ₹504
15. 15.If 7 pens cost ₹63, how much do 2 pens cost? (a) ₹126 (b) ₹58 (c) ₹27 (d) ₹18
16. 16.₹350 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹175 (b) ₹350 (c) ₹300 (d) ₹50
17. 17.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹72 (b) ₹38 (c) ₹90 (d) ₹144
18. 18.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹60 (b) ₹48 (c) ₹37 (d) ₹144
19. 19.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹161 (b) ₹46 (c) ₹230 (d) ₹92
20. 20.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 12 days (d) 6 days
21. 21.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹22 (b) ₹44 (c) ₹154 (d) ₹99
22. 22.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 15 days (d) 6 days
23. 23.If 4 pens cost ₹52, how much do 2 pens cost? (a) ₹39 (b) ₹104 (c) ₹50 (d) ₹26
24. 24.If 2 notebooks cost ₹6, how much do 4 notebooks cost? (a) ₹24 (b) ₹12 (c) ₹15 (d) ₹8
25. 25.If 5 pens cost ₹105, how much do 6 pens cost? (a) ₹630 (b) ₹106 (c) ₹126 (d) ₹147
26. 26.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹186 (b) ₹155 (c) ₹217 (d) ₹31
27. 27.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
28. 28.₹297 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹216 (d) ₹189
29. 29.If 3 notebooks cost ₹57, how much do 4 notebooks cost? (a) ₹95 (b) ₹76 (c) ₹58 (d) ₹228
30. 30.If 3 mangoes cost ₹39, how much do 6 mangoes cost? (a) ₹91 (b) ₹78 (c) ₹234 (d) ₹42
31. 31.If 7 kites cost ₹140, how much do 8 kites cost? (a) ₹1120 (b) ₹141 (c) ₹180 (d) ₹160
32. 32.If 9 pens cost ₹171, how much do 8 pens cost? (a) ₹152 (b) ₹1368 (c) ₹171 (d) ₹170
33. 33.If 5 notebooks cost ₹100, how much do 3 notebooks cost? (a) ₹80 (b) ₹60 (c) ₹300 (d) ₹98
34. 34.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 13 days (d) 22 days
35. 35.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹63 (d) ₹62
36. 36.If 9 kites cost ₹198, how much do 7 kites cost? (a) ₹176 (b) ₹196 (c) ₹1386 (d) ₹154
37. 37.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 9 days (d) 19 days
38. 38.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹260 (b) ₹40 (c) ₹360 (d) ₹160
39. 39.If 6 kites cost ₹72, how much do 11 kites cost? (a) ₹792 (b) ₹144 (c) ₹77 (d) ₹132
40. 40.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 4 days (d) 8 days

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