Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 812 · 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 7 mangoes cost ₹119, how much do 3 mangoes cost? (a) ₹68 (b) ₹357 (c) ₹51 (d) ₹115
2. 2.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹8 (d) ₹12
3. 3.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹154 (b) ₹110 (c) ₹198 (d) ₹22
4. 4.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 35 days (d) 36 days
5. 5.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 16 days (d) 13 days
6. 6.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹30 (b) ₹39 (c) ₹6 (d) ₹48
7. 7.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹35 (b) ₹42 (c) ₹7 (d) ₹28
8. 8.If 2 pens cost ₹16, how much do 3 pens cost? (a) ₹24 (b) ₹48 (c) ₹17 (d) ₹32
9. 9.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 21 days (d) 11 days
10. 10.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 5 days (c) 21 days (d) 13 days
11. 11.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 1 day
12. 12.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹72 (d) ₹45
13. 13.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 14 days (d) 18 days
14. 14.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
15. 15.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹24 (c) ₹120 (d) ₹72
16. 16.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 6 days
17. 17.If 5 mangoes cost ₹35, how much do 6 mangoes cost? (a) ₹49 (b) ₹36 (c) ₹42 (d) ₹210
18. 18.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 42 days (d) 43 days
19. 19.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 41 days (c) 20 days (d) 40 days
20. 20.If 8 pens cost ₹32, how much do 7 pens cost? (a) ₹31 (b) ₹28 (c) ₹224 (d) ₹32
21. 21.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹88 (b) ₹128 (c) ₹16 (d) ₹48
22. 22.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹250 (c) ₹450 (d) ₹50
23. 23.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 10 days (d) 17 days
24. 24.If 3 notebooks cost ₹48, how much do 10 notebooks cost? (a) ₹176 (b) ₹55 (c) ₹160 (d) ₹480
25. 25.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 2 days (d) 19 days
26. 26.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 12 days (d) 23 days
27. 27.If 9 notebooks cost ₹27, how much do 3 notebooks cost? (a) ₹21 (b) ₹81 (c) ₹9 (d) ₹12
28. 28.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹108 (d) ₹90
29. 29.If 3 kites cost ₹72, how much do 11 kites cost? (a) ₹80 (b) ₹288 (c) ₹264 (d) ₹792
30. 30.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 28 days
31. 31.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹143 (b) ₹110 (c) ₹22 (d) ₹176
32. 32.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹45 (c) ₹9 (d) ₹81
33. 33.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 3 days (d) 2 days
34. 34.If 8 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹192 (b) ₹30 (c) ₹44 (d) ₹24
35. 35.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹25 (b) ₹225 (c) ₹125 (d) ₹175
36. 36.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹42 (d) ₹18
37. 37.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹333 (d) ₹185
38. 38.If 6 kites cost ₹138, how much do 7 kites cost? (a) ₹966 (b) ₹139 (c) ₹184 (d) ₹161
39. 39.If 4 pens cost ₹32, how much do 9 pens cost? (a) ₹72 (b) ₹80 (c) ₹37 (d) ₹288
40. 40.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 11 days (d) 7 days

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