Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 234 · 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 ₹48, how much do 6 notebooks cost? (a) ₹168 (b) ₹288 (c) ₹52 (d) ₹144
2. 2.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹105 (d) ₹75
3. 3.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 5 days (c) 4 days (d) 16 days
4. 4.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
5. 5.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹108 (b) ₹168 (c) ₹48 (d) ₹24
6. 6.If 2 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹17 (b) ₹24 (c) ₹48 (d) ₹32
7. 7.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 3 days (d) 7 days
8. 8.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹100 (b) ₹75 (c) ₹125 (d) ₹25
9. 9.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹99 (b) ₹108 (c) ₹90 (d) ₹18
10. 10.₹308 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹28 (b) ₹154 (c) ₹56 (d) ₹252
11. 11.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 14 days (d) 18 days
12. 12.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹143 (b) ₹176 (c) ₹110 (d) ₹22
13. 13.If 7 notebooks cost ₹91, how much do 6 notebooks cost? (a) ₹78 (b) ₹90 (c) ₹546 (d) ₹91
14. 14.If 4 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹42 (b) ₹29 (c) ₹140 (d) ₹35
15. 15.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 26 days (d) 9 days
16. 16.If 2 pens cost ₹12, how much do 4 pens cost? (a) ₹14 (b) ₹24 (c) ₹48 (d) ₹30
17. 17.If 6 mangoes cost ₹84, how much do 8 mangoes cost? (a) ₹672 (b) ₹126 (c) ₹86 (d) ₹112
18. 18.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹36 (b) ₹37 (c) ₹45 (d) ₹9
19. 19.If 7 notebooks cost ₹49, how much do 12 notebooks cost? (a) ₹588 (b) ₹54 (c) ₹91 (d) ₹84
20. 20.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 9 days (d) 8 days
21. 21.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 13 days (d) 28 days
22. 22.If 7 kites cost ₹56, how much do 6 kites cost? (a) ₹336 (b) ₹48 (c) ₹55 (d) ₹56
23. 23.If 4 pens cost ₹76, how much do 12 pens cost? (a) ₹247 (b) ₹84 (c) ₹912 (d) ₹228
24. 24.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹195 (d) ₹240
25. 25.If 8 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹80 (b) ₹15 (c) ₹34 (d) ₹10
26. 26.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 14 days (d) 8 days
27. 27.If 9 notebooks cost ₹216, how much do 7 notebooks cost? (a) ₹214 (b) ₹192 (c) ₹1512 (d) ₹168
28. 28.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 29 days (d) 1 day
29. 29.If 2 pens cost ₹18, how much do 5 pens cost? (a) ₹21 (b) ₹90 (c) ₹45 (d) ₹54
30. 30.If 5 pens cost ₹40, how much do 6 pens cost? (a) ₹56 (b) ₹240 (c) ₹41 (d) ₹48
31. 31.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹14 (b) ₹112 (c) ₹56 (d) ₹98
32. 32.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹42 (b) ₹14 (c) ₹49 (d) ₹56
33. 33.₹341 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹279 (b) ₹62 (c) ₹310 (d) ₹31
34. 34.If 7 kites cost ₹28, how much do 6 kites cost? (a) ₹28 (b) ₹27 (c) ₹168 (d) ₹24
35. 35.If 7 pens cost ₹35, how much do 9 pens cost? (a) ₹37 (b) ₹315 (c) ₹50 (d) ₹45
36. 36.If 9 pens cost ₹36, how much do 5 pens cost? (a) ₹180 (b) ₹24 (c) ₹32 (d) ₹20
37. 37.If 9 pens cost ₹207, how much do 10 pens cost? (a) ₹253 (b) ₹2070 (c) ₹230 (d) ₹208
38. 38.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 4 days (d) 5 days
39. 39.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹78 (d) ₹65
40. 40.If 5 kites cost ₹120, how much do 3 kites cost? (a) ₹96 (b) ₹72 (c) ₹118 (d) ₹360

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