Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 654 · 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. 1.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 1 day (c) 9 days (d) 3 days
2. 2.If 5 pens cost ₹50, how much do 8 pens cost? (a) ₹80 (b) ₹53 (c) ₹400 (d) ₹90
3. 3.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹80 (b) ₹60 (c) ₹40 (d) ₹120
4. 4.If 8 pens cost ₹96, how much do 7 pens cost? (a) ₹96 (b) ₹672 (c) ₹95 (d) ₹84
5. 5.If 8 pens cost ₹32, how much do 9 pens cost? (a) ₹40 (b) ₹33 (c) ₹36 (d) ₹288
6. 6.If 6 notebooks cost ₹108, how much do 10 notebooks cost? (a) ₹180 (b) ₹198 (c) ₹1080 (d) ₹112
7. 7.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 19 days (d) 28 days
8. 8.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 18 days (c) 8 days (d) 11 days
9. 9.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 56 days (c) 20 days (d) 8 days
10. 10.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 55 days (d) 54 days
11. 11.₹168 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹24 (b) ₹84 (c) ₹168 (d) ₹144
12. 12.If 6 kites cost ₹66, how much do 2 kites cost? (a) ₹62 (b) ₹22 (c) ₹33 (d) ₹132
13. 13.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹266 (b) ₹38 (c) ₹190 (d) ₹342
14. 14.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹246 (d) ₹287
15. 15.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 21 days (d) 13 days
16. 16.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹28 (b) ₹35 (c) ₹7 (d) ₹29
17. 17.If 5 pens cost ₹125, how much do 3 pens cost? (a) ₹75 (b) ₹123 (c) ₹375 (d) ₹100
18. 18.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 13 days (d) 9 days
19. 19.If 4 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹48 (b) ₹16 (c) ₹12 (d) ₹15
20. 20.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 28 days (d) 7 days
21. 21.If 9 mangoes cost ₹225, how much do 10 mangoes cost? (a) ₹250 (b) ₹275 (c) ₹2250 (d) ₹226
22. 22.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 4 days
23. 23.₹414 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹207 (b) ₹46 (c) ₹92 (d) ₹322
24. 24.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 33 days (d) 32 days
25. 25.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹231 (b) ₹198 (c) ₹33 (d) ₹165
26. 26.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹172 (b) ₹43 (c) ₹387 (d) ₹430
27. 27.If 9 mangoes cost ₹117, how much do 4 mangoes cost? (a) ₹52 (b) ₹112 (c) ₹65 (d) ₹468
28. 28.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹55 (d) ₹60
29. 29.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹104 (b) ₹117 (c) ₹39 (d) ₹13
30. 30.If 2 mangoes cost ₹22, how much do 8 mangoes cost? (a) ₹176 (b) ₹88 (c) ₹99 (d) ₹28
31. 31.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 10 days (d) 24 days
32. 32.If 4 pens cost ₹40, how much do 12 pens cost? (a) ₹48 (b) ₹480 (c) ₹120 (d) ₹130
33. 33.If 3 notebooks cost ₹48, how much do 12 notebooks cost? (a) ₹192 (b) ₹208 (c) ₹576 (d) ₹57
34. 34.If 6 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹40 (b) ₹46 (c) ₹32 (d) ₹192
35. 35.If 7 mangoes cost ₹168, how much do 11 mangoes cost? (a) ₹288 (b) ₹264 (c) ₹172 (d) ₹1848
36. 36.If 4 notebooks cost ₹40, how much do 5 notebooks cost? (a) ₹60 (b) ₹41 (c) ₹200 (d) ₹50
37. 37.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 7 days (d) 9 days
38. 38.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹21 (c) ₹7 (d) ₹14
39. 39.₹275 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹25 (b) ₹200 (c) ₹75 (d) ₹225
40. 40.If 7 notebooks cost ₹112, how much do 4 notebooks cost? (a) ₹80 (b) ₹448 (c) ₹109 (d) ₹64

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