Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 119 · 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.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹108 (b) ₹81 (c) ₹54 (d) ₹27
2. 2.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 36 days (d) 4 days
3. 3.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹70 (d) ₹30
4. 4.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹162 (c) ₹18 (d) ₹90
5. 5.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 35 days (c) 5 days (d) 36 days
6. 6.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 24 days (d) 25 days
7. 7.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 4 days (d) 2 days
8. 8.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹11 (b) ₹66 (c) ₹55 (d) ₹77
9. 9.If 9 kites cost ₹189, how much do 11 kites cost? (a) ₹252 (b) ₹231 (c) ₹2079 (d) ₹191
10. 10.If 5 pens cost ₹125, how much do 12 pens cost? (a) ₹1500 (b) ₹132 (c) ₹325 (d) ₹300
11. 11.6 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) 8 days (d) 7 days
12. 12.If 4 mangoes cost ₹40, how much do 5 mangoes cost? (a) ₹50 (b) ₹60 (c) ₹200 (d) ₹41
13. 13.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹296 (b) ₹37 (c) ₹333 (d) ₹111
14. 14.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹11 (c) ₹5 (d) ₹10
15. 15.If 6 mangoes cost ₹144, how much do 10 mangoes cost? (a) ₹1440 (b) ₹264 (c) ₹148 (d) ₹240
16. 16.If 5 mangoes cost ₹95, how much do 6 mangoes cost? (a) ₹114 (b) ₹133 (c) ₹96 (d) ₹570
17. 17.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 17 days (d) 6 days
18. 18.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 6 days (d) 7 days
19. 19.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹117 (b) ₹156 (c) ₹195 (d) ₹39
20. 20.If 9 pens cost ₹153, how much do 2 pens cost? (a) ₹146 (b) ₹51 (c) ₹306 (d) ₹34
21. 21.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 4 days (d) 5 days
22. 22.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 5 days (d) 15 days
23. 23.If 6 notebooks cost ₹48, how much do 12 notebooks cost? (a) ₹54 (b) ₹96 (c) ₹104 (d) ₹576
24. 24.If 4 mangoes cost ₹40, how much do 10 mangoes cost? (a) ₹110 (b) ₹100 (c) ₹46 (d) ₹400
25. 25.If 6 notebooks cost ₹96, how much do 7 notebooks cost? (a) ₹672 (b) ₹128 (c) ₹97 (d) ₹112
26. 26.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 11 days (d) 21 days
27. 27.7 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) 8 days (d) 6 days
28. 28.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
29. 29.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
30. 30.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 13 days (d) 29 days
31. 31.₹84 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹56 (b) ₹42 (c) ₹28 (d) ₹84
32. 32.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 8 days (d) 10 days
33. 33.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 19 days (c) 18 days (d) 2 days
34. 34.If 5 pens cost ₹95, how much do 10 pens cost? (a) ₹950 (b) ₹209 (c) ₹100 (d) ₹190
35. 35.₹210 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹63 (b) ₹21 (c) ₹147 (d) ₹105
36. 36.If 3 kites cost ₹24, how much do 9 kites cost? (a) ₹72 (b) ₹80 (c) ₹216 (d) ₹30
37. 37.If 3 notebooks cost ₹12, how much do 8 notebooks cost? (a) ₹17 (b) ₹36 (c) ₹96 (d) ₹32
38. 38.If 8 pens cost ₹88, how much do 4 pens cost? (a) ₹84 (b) ₹55 (c) ₹44 (d) ₹352
39. 39.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 12 days
40. 40.If 3 mangoes cost ₹15, how much do 11 mangoes cost? (a) ₹55 (b) ₹165 (c) ₹23 (d) ₹60

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