Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 205 · 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 3 pens cost ₹42, how much do 2 pens cost? (a) ₹84 (b) ₹41 (c) ₹42 (d) ₹28
2. 2.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 13 days (d) 12 days
3. 3.If 2 pens cost ₹26, how much do 9 pens cost? (a) ₹234 (b) ₹117 (c) ₹33 (d) ₹130
4. 4.If 2 pens cost ₹48, how much do 7 pens cost? (a) ₹192 (b) ₹336 (c) ₹53 (d) ₹168
5. 5.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹168 (b) ₹378 (c) ₹273 (d) ₹42
6. 6.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 36 days (d) 6 days
7. 7.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹258 (b) ₹172 (c) ₹215 (d) ₹43
8. 8.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹30 (b) ₹40 (c) ₹35 (d) ₹10
9. 9.If 9 mangoes cost ₹54, how much do 7 mangoes cost? (a) ₹42 (b) ₹48 (c) ₹52 (d) ₹378
10. 10.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹7 (c) ₹63 (d) ₹35
11. 11.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 5 days (d) 16 days
12. 12.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹312 (d) ₹384
13. 13.If 2 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹42 (b) ₹56 (c) ₹29 (d) ₹84
14. 14.If 8 kites cost ₹56, how much do 3 kites cost? (a) ₹168 (b) ₹21 (c) ₹28 (d) ₹51
15. 15.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 11 days (c) 8 days (d) 7 days
16. 16.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 8 days (d) 9 days
17. 17.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹66 (d) ₹77
18. 18.If 9 kites cost ₹90, how much do 8 kites cost? (a) ₹89 (b) ₹720 (c) ₹80 (d) ₹90
19. 19.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 3 days (d) 12 days
20. 20.If 9 notebooks cost ₹126, how much do 4 notebooks cost? (a) ₹121 (b) ₹70 (c) ₹56 (d) ₹504
21. 21.If 7 pens cost ₹21, how much do 11 pens cost? (a) ₹36 (b) ₹231 (c) ₹33 (d) ₹25
22. 22.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 18 days (d) 6 days
23. 23.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 2 days (d) 13 days
24. 24.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹156 (b) ₹24 (c) ₹120 (d) ₹192
25. 25.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 11 days (d) 1 day
26. 26.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 27 days (d) 11 days
27. 27.If 7 kites cost ₹42, how much do 4 kites cost? (a) ₹39 (b) ₹168 (c) ₹30 (d) ₹24
28. 28.If 8 pens cost ₹136, how much do 3 pens cost? (a) ₹68 (b) ₹131 (c) ₹408 (d) ₹51
29. 29.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹162 (b) ₹288 (c) ₹36 (d) ₹324
30. 30.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹72 (d) ₹36
31. 31.₹350 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹175 (d) ₹105
32. 32.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹79 (b) ₹91 (c) ₹78 (d) ₹13
33. 33.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹84 (d) ₹63
34. 34.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹120 (c) ₹24 (d) ₹72
35. 35.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 11 days (d) 10 days
36. 36.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹13 (b) ₹18 (c) ₹36 (d) ₹24
37. 37.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 4 days (d) 7 days
38. 38.If 2 mangoes cost ₹38, how much do 8 mangoes cost? (a) ₹44 (b) ₹171 (c) ₹152 (d) ₹304
39. 39.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹84 (b) ₹21 (c) ₹147 (d) ₹168
40. 40.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 24 days (b) 18 days (c) 7 days (d) 6 days

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