Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 587 · 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 4 pens cost ₹12, how much do 2 pens cost? (a) ₹24 (b) ₹6 (c) ₹9 (d) ₹10
2. 2.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹6 (b) ₹15 (c) ₹18 (d) ₹12
3. 3.If 2 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹36 (b) ₹280 (c) ₹154 (d) ₹140
4. 4.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹96 (d) ₹56
5. 5.If 3 pens cost ₹24, how much do 10 pens cost? (a) ₹80 (b) ₹31 (c) ₹240 (d) ₹88
6. 6.6 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) 5 days (d) 4 days
7. 7.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 28 days (d) 27 days
8. 8.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹56 (b) ₹64 (c) ₹48 (d) ₹16
9. 9.₹414 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹322 (d) ₹207
10. 10.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹240 (c) ₹30 (d) ₹150
11. 11.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹119 (b) ₹136 (c) ₹68 (d) ₹17
12. 12.₹96 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹96 (d) ₹84
13. 13.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 16 days (d) 7 days
14. 14.If 2 notebooks cost ₹36, how much do 5 notebooks cost? (a) ₹39 (b) ₹180 (c) ₹108 (d) ₹90
15. 15.If 9 pens cost ₹144, how much do 12 pens cost? (a) ₹208 (b) ₹1728 (c) ₹147 (d) ₹192
16. 16.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹325 (d) ₹400
17. 17.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 26 days (d) 27 days
18. 18.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹180 (b) ₹105 (c) ₹210 (d) ₹30
19. 19.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 9 days (d) 19 days
20. 20.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹48 (c) ₹8 (d) ₹44
21. 21.If 3 notebooks cost ₹60, how much do 10 notebooks cost? (a) ₹67 (b) ₹200 (c) ₹600 (d) ₹220
22. 22.If 9 notebooks cost ₹108, how much do 10 notebooks cost? (a) ₹109 (b) ₹132 (c) ₹120 (d) ₹1080
23. 23.If 2 kites cost ₹46, how much do 8 kites cost? (a) ₹207 (b) ₹368 (c) ₹184 (d) ₹52
24. 24.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹48 (d) ₹36
25. 25.If 5 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹180 (b) ₹58 (c) ₹48 (d) ₹36
26. 26.If 8 pens cost ₹144, how much do 11 pens cost? (a) ₹198 (b) ₹216 (c) ₹1584 (d) ₹147
27. 27.If 2 pens cost ₹24, how much do 12 pens cost? (a) ₹288 (b) ₹156 (c) ₹144 (d) ₹34
28. 28.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹230 (b) ₹322 (c) ₹46 (d) ₹138
29. 29.If 7 pens cost ₹84, how much do 6 pens cost? (a) ₹72 (b) ₹84 (c) ₹504 (d) ₹83
30. 30.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 21 days (b) 7 days (c) 6 days (d) 9 days
31. 31.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
32. 32.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹78 (b) ₹26 (c) ₹130 (d) ₹182
33. 33.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 54 days (b) 19 days (c) 5 days (d) 55 days
34. 34.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹243 (d) ₹216
35. 35.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹90 (b) ₹30 (c) ₹150 (d) ₹120
36. 36.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 14 days (d) 8 days
37. 37.If 2 kites cost ₹14, how much do 10 kites cost? (a) ₹70 (b) ₹22 (c) ₹140 (d) ₹77
38. 38.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 4 days (d) 16 days
39. 39.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 8 days (d) 6 days
40. 40.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 5 days (d) 16 days

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