Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 782 · 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.₹495 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹135 (d) ₹360
2. 2.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 17 days (d) 6 days
3. 3.If 7 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹129 (b) ₹1260 (c) ₹198 (d) ₹180
4. 4.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 12 days (d) 4 days
5. 5.If 8 pens cost ₹48, how much do 9 pens cost? (a) ₹54 (b) ₹60 (c) ₹432 (d) ₹49
6. 6.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹189 (c) ₹168 (d) ₹42
7. 7.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 16 days
8. 8.If 4 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹34 (b) ₹27 (c) ₹18 (d) ₹72
9. 9.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 25 days (c) 4 days (d) 24 days
10. 10.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹8 (b) ₹12 (c) ₹16 (d) ₹24
11. 11.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹280 (b) ₹315 (c) ₹35 (d) ₹175
12. 12.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹176 (b) ₹143 (c) ₹22 (d) ₹110
13. 13.If 3 notebooks cost ₹27, how much do 2 notebooks cost? (a) ₹54 (b) ₹27 (c) ₹26 (d) ₹18
14. 14.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹148 (b) ₹111 (c) ₹185 (d) ₹37
15. 15.If 8 mangoes cost ₹200, how much do 2 mangoes cost? (a) ₹50 (b) ₹194 (c) ₹75 (d) ₹400
16. 16.If 5 notebooks cost ₹15, how much do 10 notebooks cost? (a) ₹33 (b) ₹20 (c) ₹150 (d) ₹30
17. 17.If 4 kites cost ₹40, how much do 5 kites cost? (a) ₹200 (b) ₹50 (c) ₹41 (d) ₹60
18. 18.If 3 kites cost ₹69, how much do 6 kites cost? (a) ₹414 (b) ₹138 (c) ₹72 (d) ₹161
19. 19.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 11 days
20. 20.₹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
21. 21.If 3 notebooks cost ₹48, how much do 7 notebooks cost? (a) ₹112 (b) ₹336 (c) ₹52 (d) ₹128
22. 22.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 7 days (d) 11 days
23. 23.If 8 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹240 (b) ₹35 (c) ₹38 (d) ₹30
24. 24.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 9 days (d) 17 days
25. 25.If 6 pens cost ₹144, how much do 7 pens cost? (a) ₹168 (b) ₹1008 (c) ₹192 (d) ₹145
26. 26.If 3 mangoes cost ₹30, how much do 12 mangoes cost? (a) ₹39 (b) ₹360 (c) ₹120 (d) ₹130
27. 27.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹46 (b) ₹184 (c) ₹138 (d) ₹92
28. 28.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 13 days (d) 15 days
29. 29.If 4 kites cost ₹80, how much do 11 kites cost? (a) ₹880 (b) ₹87 (c) ₹220 (d) ₹240
30. 30.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 5 days (d) 10 days
31. 31.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹104 (d) ₹64
32. 32.If 4 kites cost ₹64, how much do 7 kites cost? (a) ₹67 (b) ₹448 (c) ₹112 (d) ₹128
33. 33.If 8 kites cost ₹32, how much do 3 kites cost? (a) ₹16 (b) ₹96 (c) ₹27 (d) ₹12
34. 34.If 4 notebooks cost ₹44, how much do 6 notebooks cost? (a) ₹46 (b) ₹66 (c) ₹77 (d) ₹264
35. 35.If 7 pens cost ₹70, how much do 12 pens cost? (a) ₹75 (b) ₹840 (c) ₹130 (d) ₹120
36. 36.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 15 days (c) 5 days (d) 36 days
37. 37.₹138 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹69 (b) ₹23 (c) ₹138 (d) ₹115
38. 38.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 16 days (d) 9 days
39. 39.₹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
40. 40.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹70 (d) ₹90

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