Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 188 · 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 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
2. 2.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹180 (b) ₹126 (c) ₹72 (d) ₹36
3. 3.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 13 days (d) 6 days
4. 4.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 11 days (d) 17 days
5. 5.If 9 mangoes cost ₹90, how much do 3 mangoes cost? (a) ₹40 (b) ₹270 (c) ₹84 (d) ₹30
6. 6.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 1 day (d) 28 days
7. 7.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹81 (b) ₹162 (c) ₹135 (d) ₹27
8. 8.₹182 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹26 (b) ₹91 (c) ₹52 (d) ₹130
9. 9.If 3 kites cost ₹69, how much do 9 kites cost? (a) ₹230 (b) ₹75 (c) ₹207 (d) ₹621
10. 10.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 2 days (d) 4 days
11. 11.If 3 notebooks cost ₹33, how much do 12 notebooks cost? (a) ₹132 (b) ₹143 (c) ₹42 (d) ₹396
12. 12.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 12 days (d) 20 days
13. 13.If 7 notebooks cost ₹168, how much do 3 notebooks cost? (a) ₹504 (b) ₹96 (c) ₹72 (d) ₹164
14. 14.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 1 day (d) 8 days
15. 15.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹10 (c) ₹55 (d) ₹50
16. 16.If 8 notebooks cost ₹200, how much do 9 notebooks cost? (a) ₹1800 (b) ₹250 (c) ₹201 (d) ₹225
17. 17.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 13 days (d) 9 days
18. 18.If 3 mangoes cost ₹72, how much do 8 mangoes cost? (a) ₹216 (b) ₹192 (c) ₹576 (d) ₹77
19. 19.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹238 (d) ₹102
20. 20.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹40 (c) ₹50 (d) ₹20
21. 21.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹10 (b) ₹15 (c) ₹20 (d) ₹5
22. 22.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 11 days (d) 1 day
23. 23.If 3 kites cost ₹66, how much do 12 kites cost? (a) ₹264 (b) ₹75 (c) ₹792 (d) ₹286
24. 24.If 4 kites cost ₹84, how much do 7 kites cost? (a) ₹147 (b) ₹87 (c) ₹168 (d) ₹588
25. 25.If 4 pens cost ₹68, how much do 11 pens cost? (a) ₹204 (b) ₹748 (c) ₹187 (d) ₹75
26. 26.If 6 pens cost ₹54, how much do 2 pens cost? (a) ₹108 (b) ₹27 (c) ₹50 (d) ₹18
27. 27.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹64 (b) ₹128 (c) ₹16 (d) ₹112
28. 28.8 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
29. 29.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹36 (b) ₹108 (c) ₹198 (d) ₹288
30. 30.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹93 (d) ₹124
31. 31.If 7 pens cost ₹28, how much do 11 pens cost? (a) ₹44 (b) ₹308 (c) ₹48 (d) ₹32
32. 32.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 40 days (c) 16 days (d) 41 days
33. 33.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹32 (b) ₹24 (c) ₹16 (d) ₹48
34. 34.If 2 notebooks cost ₹10, how much do 7 notebooks cost? (a) ₹15 (b) ₹70 (c) ₹40 (d) ₹35
35. 35.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹225 (b) ₹200 (c) ₹50 (d) ₹250
36. 36.If 4 pens cost ₹100, how much do 3 pens cost? (a) ₹99 (b) ₹300 (c) ₹75 (d) ₹100
37. 37.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹150 (b) ₹180 (c) ₹30 (d) ₹90
38. 38.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 4 days (d) 9 days
39. 39.If 9 pens cost ₹225, how much do 3 pens cost? (a) ₹219 (b) ₹675 (c) ₹100 (d) ₹75
40. 40.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 9 days

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