Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 643 · 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.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹112 (b) ₹80 (c) ₹16 (d) ₹144
2. 2.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 14 days (c) 21 days (d) 10 days
3. 3.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 7 days
4. 4.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 16 days (d) 11 days
5. 5.If 5 kites cost ₹15, how much do 7 kites cost? (a) ₹24 (b) ₹105 (c) ₹17 (d) ₹21
6. 6.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
7. 7.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹38 (b) ₹342 (c) ₹190 (d) ₹266
8. 8.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹25 (c) ₹5 (d) ₹20
9. 9.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 16 days (d) 4 days
10. 10.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹42 (d) ₹21
11. 11.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹130 (b) ₹208 (c) ₹26 (d) ₹169
12. 12.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 1 day (d) 21 days
13. 13.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 24 days (d) 17 days
14. 14.If 7 mangoes cost ₹70, how much do 9 mangoes cost? (a) ₹100 (b) ₹72 (c) ₹630 (d) ₹90
15. 15.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹102 (c) ₹34 (d) ₹68
16. 16.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹325 (b) ₹50 (c) ₹450 (d) ₹200
17. 17.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 2 days (d) 1 day
18. 18.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹56 (d) ₹57
19. 19.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 9 days (d) 17 days
20. 20.4 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
21. 21.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 4 days (d) 6 days
22. 22.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 7 days (c) 19 days (d) 52 days
23. 23.If 9 notebooks cost ₹90, how much do 10 notebooks cost? (a) ₹900 (b) ₹100 (c) ₹110 (d) ₹91
24. 24.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹132 (b) ₹121 (c) ₹110 (d) ₹22
25. 25.If 2 notebooks cost ₹6, how much do 3 notebooks cost? (a) ₹18 (b) ₹7 (c) ₹12 (d) ₹9
26. 26.If 4 kites cost ₹92, how much do 2 kites cost? (a) ₹90 (b) ₹46 (c) ₹69 (d) ₹184
27. 27.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 19 days (d) 6 days
28. 28.If 6 pens cost ₹138, how much do 10 pens cost? (a) ₹1380 (b) ₹230 (c) ₹142 (d) ₹253
29. 29.If 2 notebooks cost ₹12, how much do 3 notebooks cost? (a) ₹24 (b) ₹36 (c) ₹18 (d) ₹13
30. 30.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹299 (b) ₹414 (c) ₹46 (d) ₹184
31. 31.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹60 (d) ₹30
32. 32.If 4 pens cost ₹84, how much do 5 pens cost? (a) ₹126 (b) ₹85 (c) ₹105 (d) ₹420
33. 33.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 17 days (d) 11 days
34. 34.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
35. 35.If 3 kites cost ₹66, how much do 7 kites cost? (a) ₹70 (b) ₹154 (c) ₹176 (d) ₹462
36. 36.If 5 kites cost ₹100, how much do 2 kites cost? (a) ₹200 (b) ₹40 (c) ₹97 (d) ₹60
37. 37.If 5 kites cost ₹90, how much do 4 kites cost? (a) ₹360 (b) ₹90 (c) ₹72 (d) ₹89
38. 38.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 46 days (b) 17 days (c) 3 days (d) 45 days
39. 39.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹74 (b) ₹148 (c) ₹37 (d) ₹111
40. 40.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days

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