Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 496 · 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 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 9 days
2. 2.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 21 days (d) 22 days
3. 3.If 7 pens cost ₹49, how much do 3 pens cost? (a) ₹45 (b) ₹28 (c) ₹21 (d) ₹147
4. 4.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 15 days (d) 16 days
5. 5.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹175 (c) ₹35 (d) ₹140
6. 6.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 3 days
7. 7.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹91 (b) ₹112 (c) ₹14 (d) ₹70
8. 8.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 3 days (d) 6 days
9. 9.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹336 (b) ₹48 (c) ₹288 (d) ₹168
10. 10.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹15 (d) ₹135
11. 11.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 20 days (c) 8 days (d) 56 days
12. 12.If 6 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹80 (b) ₹51 (c) ₹432 (d) ₹72
13. 13.₹451 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹328 (d) ₹287
14. 14.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 9 days (d) 22 days
15. 15.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 17 days (d) 7 days
16. 16.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹20 (b) ₹110 (c) ₹180 (d) ₹40
17. 17.If 5 mangoes cost ₹30, how much do 12 mangoes cost? (a) ₹78 (b) ₹37 (c) ₹360 (d) ₹72
18. 18.If 6 pens cost ₹36, how much do 9 pens cost? (a) ₹60 (b) ₹324 (c) ₹39 (d) ₹54
19. 19.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 9 days
20. 20.If 9 pens cost ₹216, how much do 2 pens cost? (a) ₹72 (b) ₹48 (c) ₹432 (d) ₹209
21. 21.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 36 days (d) 35 days
22. 22.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 15 days (d) 5 days
23. 23.If 3 pens cost ₹36, how much do 5 pens cost? (a) ₹38 (b) ₹72 (c) ₹60 (d) ₹180
24. 24.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹129 (b) ₹172 (c) ₹43 (d) ₹215
25. 25.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
26. 26.If 5 pens cost ₹40, how much do 9 pens cost? (a) ₹44 (b) ₹360 (c) ₹80 (d) ₹72
27. 27.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹8 (d) ₹32
28. 28.If 7 kites cost ₹21, how much do 8 kites cost? (a) ₹24 (b) ₹168 (c) ₹22 (d) ₹27
29. 29.₹495 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹180 (b) ₹45 (c) ₹360 (d) ₹315
30. 30.If 9 mangoes cost ₹99, how much do 12 mangoes cost? (a) ₹132 (b) ₹143 (c) ₹1188 (d) ₹102
31. 31.If 4 notebooks cost ₹100, how much do 12 notebooks cost? (a) ₹108 (b) ₹1200 (c) ₹325 (d) ₹300
32. 32.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹100 (c) ₹150 (d) ₹125
33. 33.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 29 days (c) 13 days (d) 28 days
34. 34.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹117 (b) ₹195 (c) ₹39 (d) ₹234
35. 35.If 8 notebooks cost ₹24, how much do 11 notebooks cost? (a) ₹27 (b) ₹36 (c) ₹264 (d) ₹33
36. 36.₹494 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹247 (d) ₹304
37. 37.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 12 days (d) 3 days
38. 38.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 18 days (d) 24 days
39. 39.If 5 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹37 (b) ₹24 (c) ₹16 (d) ₹80
40. 40.If 4 mangoes cost ₹84, how much do 6 mangoes cost? (a) ₹86 (b) ₹126 (c) ₹147 (d) ₹504

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