Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 224 · 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 2 notebooks cost ₹10, how much do 3 notebooks cost? (a) ₹20 (b) ₹15 (c) ₹11 (d) ₹30
2. 2.If 9 kites cost ₹189, how much do 5 kites cost? (a) ₹105 (b) ₹945 (c) ₹185 (d) ₹126
3. 3.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 12 days (d) 3 days
4. 4.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 20 days (d) 13 days
5. 5.₹432 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹216 (b) ₹384 (c) ₹432 (d) ₹48
6. 6.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹140 (b) ₹14 (c) ₹126 (d) ₹70
7. 7.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 13 days (d) 7 days
8. 8.5 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
9. 9.If 6 notebooks cost ₹138, how much do 7 notebooks cost? (a) ₹139 (b) ₹161 (c) ₹184 (d) ₹966
10. 10.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 44 days (c) 17 days (d) 45 days
11. 11.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 4 days (d) 8 days
12. 12.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹56 (c) ₹14 (d) ₹28
13. 13.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 1 day (d) 7 days
14. 14.If 2 notebooks cost ₹8, how much do 4 notebooks cost? (a) ₹20 (b) ₹32 (c) ₹10 (d) ₹16
15. 15.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 19 days (c) 11 days (d) 27 days
16. 16.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 5 days
17. 17.If 4 pens cost ₹40, how much do 3 pens cost? (a) ₹120 (b) ₹30 (c) ₹40 (d) ₹39
18. 18.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹126 (d) ₹72
19. 19.If 8 kites cost ₹48, how much do 2 kites cost? (a) ₹42 (b) ₹18 (c) ₹96 (d) ₹12
20. 20.If 5 notebooks cost ₹100, how much do 2 notebooks cost? (a) ₹60 (b) ₹200 (c) ₹40 (d) ₹97
21. 21.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹65 (b) ₹90 (c) ₹40 (d) ₹10
22. 22.If 3 mangoes cost ₹57, how much do 11 mangoes cost? (a) ₹209 (b) ₹65 (c) ₹228 (d) ₹627
23. 23.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 31 days (c) 30 days (d) 13 days
24. 24.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 2 days (d) 9 days
25. 25.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹294 (c) ₹42 (d) ₹231
26. 26.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹34 (d) ₹68
27. 27.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹171 (b) ₹38 (c) ₹19 (d) ₹190
28. 28.If 3 notebooks cost ₹21, how much do 10 notebooks cost? (a) ₹28 (b) ₹210 (c) ₹77 (d) ₹70
29. 29.If 3 kites cost ₹45, how much do 8 kites cost? (a) ₹50 (b) ₹360 (c) ₹120 (d) ₹135
30. 30.If 7 pens cost ₹168, how much do 10 pens cost? (a) ₹264 (b) ₹240 (c) ₹1680 (d) ₹171
31. 31.If 6 mangoes cost ₹72, how much do 12 mangoes cost? (a) ₹864 (b) ₹156 (c) ₹78 (d) ₹144
32. 32.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 11 days (d) 15 days
33. 33.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 16 days (d) 15 days
34. 34.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 9 days
35. 35.If 2 pens cost ₹38, how much do 12 pens cost? (a) ₹456 (b) ₹228 (c) ₹48 (d) ₹247
36. 36.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 19 days (d) 10 days
37. 37.If 9 mangoes cost ₹90, how much do 11 mangoes cost? (a) ₹92 (b) ₹120 (c) ₹110 (d) ₹990
38. 38.₹165 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹33 (b) ₹66 (c) ₹132 (d) ₹99
39. 39.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹65 (c) ₹10 (d) ₹80
40. 40.If 3 mangoes cost ₹69, how much do 6 mangoes cost? (a) ₹72 (b) ₹138 (c) ₹414 (d) ₹161

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