Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 560 · 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. 1.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 6 days (d) 4 days
2. 2.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹164 (b) ₹123 (c) ₹41 (d) ₹82
3. 3.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹200 (d) ₹280
4. 4.If 6 mangoes cost ₹144, how much do 9 mangoes cost? (a) ₹240 (b) ₹147 (c) ₹1296 (d) ₹216
5. 5.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 8 days (d) 9 days
6. 6.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹173 (b) ₹215 (c) ₹172 (d) ₹43
7. 7.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 14 days (c) 6 days (d) 30 days
8. 8.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹360 (d) ₹225
9. 9.If 5 kites cost ₹65, how much do 3 kites cost? (a) ₹195 (b) ₹52 (c) ₹63 (d) ₹39
10. 10.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 3 days (d) 4 days
11. 11.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 13 days (d) 11 days
12. 12.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹40 (b) ₹80 (c) ₹120 (d) ₹60
13. 13.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 14 days (d) 8 days
14. 14.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹333 (b) ₹370 (c) ₹148 (d) ₹37
15. 15.₹360 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹280 (b) ₹80 (c) ₹40 (d) ₹180
16. 16.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 11 days (d) 3 days
17. 17.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 4 days (d) 3 days
18. 18.If 2 pens cost ₹50, how much do 7 pens cost? (a) ₹350 (b) ₹175 (c) ₹200 (d) ₹55
19. 19.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹215 (b) ₹301 (c) ₹43 (d) ₹387
20. 20.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 24 days (c) 25 days (d) 2 days
21. 21.If 8 mangoes cost ₹104, how much do 7 mangoes cost? (a) ₹104 (b) ₹91 (c) ₹728 (d) ₹103
22. 22.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 4 days (d) 11 days
23. 23.If 6 notebooks cost ₹108, how much do 2 notebooks cost? (a) ₹216 (b) ₹36 (c) ₹54 (d) ₹104
24. 24.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 10 days (d) 11 days
25. 25.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹36 (d) ₹40
26. 26.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 16 days (d) 11 days
27. 27.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 7 days
28. 28.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹44 (b) ₹22 (c) ₹33 (d) ₹11
29. 29.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹112 (b) ₹16 (c) ₹96 (d) ₹56
30. 30.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹117 (b) ₹195 (c) ₹273 (d) ₹39
31. 31.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹96 (d) ₹64
32. 32.₹176 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹64 (b) ₹88 (c) ₹112 (d) ₹16
33. 33.If 6 pens cost ₹60, how much do 7 pens cost? (a) ₹420 (b) ₹70 (c) ₹80 (d) ₹61
34. 34.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹161 (d) ₹92
35. 35.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹215 (b) ₹430 (c) ₹387 (d) ₹43
36. 36.If 3 notebooks cost ₹27, how much do 2 notebooks cost? (a) ₹26 (b) ₹18 (c) ₹27 (d) ₹54
37. 37.If 3 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹68 (b) ₹504 (c) ₹189 (d) ₹168
38. 38.If 8 mangoes cost ₹64, how much do 9 mangoes cost? (a) ₹65 (b) ₹72 (c) ₹576 (d) ₹80
39. 39.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹324 (b) ₹252 (c) ₹180 (d) ₹36
40. 40.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹45 (d) ₹27

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