Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 879 · 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 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹81 (b) ₹720 (c) ₹90 (d) ₹100
2. 2.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 8 days (d) 9 days
3. 3.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹10 (b) ₹25 (c) ₹40 (d) ₹50
4. 4.If 2 notebooks cost ₹20, how much do 5 notebooks cost? (a) ₹60 (b) ₹23 (c) ₹100 (d) ₹50
5. 5.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹20 (c) ₹25 (d) ₹5
6. 6.If 3 mangoes cost ₹66, how much do 4 mangoes cost? (a) ₹67 (b) ₹264 (c) ₹88 (d) ₹110
7. 7.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹115 (d) ₹138
8. 8.If 2 kites cost ₹46, how much do 5 kites cost? (a) ₹138 (b) ₹230 (c) ₹49 (d) ₹115
9. 9.₹234 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹117 (d) ₹182
10. 10.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 14 days (c) 24 days (d) 25 days
11. 11.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹162 (b) ₹90 (c) ₹18 (d) ₹180
12. 12.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 52 days (d) 7 days
13. 13.If 8 pens cost ₹176, how much do 10 pens cost? (a) ₹242 (b) ₹178 (c) ₹1760 (d) ₹220
14. 14.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹162 (c) ₹126 (d) ₹18
15. 15.If 8 kites cost ₹88, how much do 2 kites cost? (a) ₹176 (b) ₹82 (c) ₹22 (d) ₹33
16. 16.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 11 days (d) 26 days
17. 17.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 19 days (d) 7 days
18. 18.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 11 days (d) 3 days
19. 19.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹48 (d) ₹36
20. 20.If 7 pens cost ₹28, how much do 8 pens cost? (a) ₹224 (b) ₹32 (c) ₹29 (d) ₹36
21. 21.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 7 days (d) 1 day
22. 22.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹16 (b) ₹88 (c) ₹48 (d) ₹128
23. 23.If 8 kites cost ₹32, how much do 9 kites cost? (a) ₹33 (b) ₹40 (c) ₹288 (d) ₹36
24. 24.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹50 (b) ₹45 (c) ₹5 (d) ₹20
25. 25.If 7 pens cost ₹154, how much do 10 pens cost? (a) ₹220 (b) ₹157 (c) ₹242 (d) ₹1540
26. 26.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 16 days (d) 14 days
27. 27.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹20 (d) ₹40
28. 28.₹210 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹60 (d) ₹105
29. 29.If 9 kites cost ₹45, how much do 5 kites cost? (a) ₹25 (b) ₹225 (c) ₹41 (d) ₹30
30. 30.If 6 pens cost ₹84, how much do 7 pens cost? (a) ₹112 (b) ₹85 (c) ₹98 (d) ₹588
31. 31.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 18 days (d) 8 days
32. 32.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 35 days (d) 19 days
33. 33.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 13 days (d) 12 days
34. 34.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 15 days (d) 4 days
35. 35.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 7 days (d) 17 days
36. 36.If 8 mangoes cost ₹56, how much do 4 mangoes cost? (a) ₹52 (b) ₹224 (c) ₹35 (d) ₹28
37. 37.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹63 (c) ₹7 (d) ₹56
38. 38.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 7 days (d) 9 days
39. 39.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 28 days
40. 40.If 9 kites cost ₹27, how much do 3 kites cost? (a) ₹21 (b) ₹12 (c) ₹81 (d) ₹9

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