Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 835 · 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 pens cost ₹91, how much do 8 pens cost? (a) ₹104 (b) ₹92 (c) ₹728 (d) ₹117
2. 2.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 14 days (d) 20 days
3. 3.If 2 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹31 (b) ₹90 (c) ₹45 (d) ₹60
4. 4.₹320 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹280 (c) ₹160 (d) ₹320
5. 5.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 7 days
6. 6.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹8 (b) ₹64 (c) ₹56 (d) ₹32
7. 7.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 3 days (d) 7 days
8. 8.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 15 days (d) 6 days
9. 9.If 9 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹360 (b) ₹44 (c) ₹40 (d) ₹37
10. 10.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹161 (b) ₹230 (c) ₹92 (d) ₹46
11. 11.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
12. 12.If 2 notebooks cost ₹34, how much do 4 notebooks cost? (a) ₹136 (b) ₹85 (c) ₹68 (d) ₹36
13. 13.If 3 kites cost ₹51, how much do 9 kites cost? (a) ₹170 (b) ₹57 (c) ₹153 (d) ₹459
14. 14.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 21 days (d) 22 days
15. 15.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 11 days (d) 13 days
16. 16.If 2 pens cost ₹20, how much do 11 pens cost? (a) ₹120 (b) ₹110 (c) ₹220 (d) ₹29
17. 17.If 9 kites cost ₹171, how much do 10 kites cost? (a) ₹209 (b) ₹190 (c) ₹172 (d) ₹1710
18. 18.If 3 notebooks cost ₹9, how much do 2 notebooks cost? (a) ₹6 (b) ₹8 (c) ₹18 (d) ₹9
19. 19.If 8 kites cost ₹152, how much do 7 kites cost? (a) ₹1064 (b) ₹152 (c) ₹133 (d) ₹151
20. 20.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹25 (b) ₹100 (c) ₹75 (d) ₹50
21. 21.If 6 pens cost ₹138, how much do 8 pens cost? (a) ₹207 (b) ₹184 (c) ₹1104 (d) ₹140
22. 22.₹216 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹189 (d) ₹216
23. 23.If 3 kites cost ₹69, how much do 6 kites cost? (a) ₹161 (b) ₹72 (c) ₹414 (d) ₹138
24. 24.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 9 days (d) 8 days
25. 25.If 9 kites cost ₹54, how much do 3 kites cost? (a) ₹24 (b) ₹162 (c) ₹48 (d) ₹18
26. 26.₹260 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹260 (b) ₹130 (c) ₹234 (d) ₹26
27. 27.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹165 (c) ₹180 (d) ₹150
28. 28.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 12 days (c) 24 days (d) 4 days
29. 29.₹133 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹76 (d) ₹95
30. 30.If 5 pens cost ₹90, how much do 10 pens cost? (a) ₹900 (b) ₹180 (c) ₹95 (d) ₹198
31. 31.If 6 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹420 (b) ₹61 (c) ₹70 (d) ₹80
32. 32.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹180 (b) ₹135 (c) ₹45 (d) ₹225
33. 33.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 6 days (d) 24 days
34. 34.If 8 mangoes cost ₹120, how much do 4 mangoes cost? (a) ₹75 (b) ₹60 (c) ₹480 (d) ₹116
35. 35.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹14 (d) ₹42
36. 36.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 8 days (d) 9 days
37. 37.If 6 mangoes cost ₹108, how much do 4 mangoes cost? (a) ₹90 (b) ₹106 (c) ₹72 (d) ₹432
38. 38.If 5 kites cost ₹30, how much do 9 kites cost? (a) ₹270 (b) ₹54 (c) ₹34 (d) ₹60
39. 39.If 4 kites cost ₹16, how much do 8 kites cost? (a) ₹32 (b) ₹20 (c) ₹128 (d) ₹36
40. 40.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 27 days (d) 3 days

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