Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 5 · 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.₹72 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹36 (b) ₹54 (c) ₹18 (d) ₹72
2. 2.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 5 days
3. 3.If 4 kites cost ₹100, how much do 2 kites cost? (a) ₹98 (b) ₹75 (c) ₹50 (d) ₹200
4. 4.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹165 (d) ₹210
5. 5.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹189 (d) ₹27
6. 6.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹273 (b) ₹336 (c) ₹42 (d) ₹210
7. 7.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹74 (b) ₹296 (c) ₹259 (d) ₹37
8. 8.₹405 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹360 (d) ₹315
9. 9.If 3 kites cost ₹30, how much do 12 kites cost? (a) ₹120 (b) ₹130 (c) ₹39 (d) ₹360
10. 10.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹14 (b) ₹112 (c) ₹91 (d) ₹70
11. 11.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹60 (b) ₹54 (c) ₹48 (d) ₹12
12. 12.If 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹81 (b) ₹100 (c) ₹720 (d) ₹90
13. 13.If 6 pens cost ₹78, how much do 3 pens cost? (a) ₹234 (b) ₹52 (c) ₹39 (d) ₹75
14. 14.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 61 days (c) 60 days (d) 21 days
15. 15.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 2 days (d) 7 days
16. 16.If 4 kites cost ₹96, how much do 9 kites cost? (a) ₹240 (b) ₹101 (c) ₹216 (d) ₹864
17. 17.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 5 days (d) 4 days
18. 18.If 2 pens cost ₹26, how much do 6 pens cost? (a) ₹78 (b) ₹91 (c) ₹156 (d) ₹30
19. 19.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 12 days (d) 13 days
20. 20.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 13 days
21. 21.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹68 (b) ₹102 (c) ₹34 (d) ₹51
22. 22.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹54 (b) ₹6 (c) ₹27 (d) ₹48
23. 23.If 7 mangoes cost ₹56, how much do 10 mangoes cost? (a) ₹80 (b) ₹59 (c) ₹560 (d) ₹88
24. 24.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹20 (b) ₹50 (c) ₹10 (d) ₹35
25. 25.If 2 pens cost ₹26, how much do 12 pens cost? (a) ₹169 (b) ₹36 (c) ₹156 (d) ₹312
26. 26.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹21 (d) ₹189
27. 27.If 4 pens cost ₹36, how much do 9 pens cost? (a) ₹324 (b) ₹81 (c) ₹41 (d) ₹90
28. 28.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 13 days
29. 29.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹23 (b) ₹230 (c) ₹92 (d) ₹207
30. 30.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 6 days
31. 31.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 20 days (c) 21 days (d) 14 days
32. 32.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹135 (d) ₹189
33. 33.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 7 days
34. 34.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹98 (d) ₹70
35. 35.If 4 mangoes cost ₹64, how much do 12 mangoes cost? (a) ₹208 (b) ₹768 (c) ₹72 (d) ₹192
36. 36.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹27 (d) ₹30
37. 37.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 34 days (c) 17 days (d) 33 days
38. 38.If 8 pens cost ₹88, how much do 3 pens cost? (a) ₹264 (b) ₹83 (c) ₹33 (d) ₹44
39. 39.If 3 mangoes cost ₹63, how much do 7 mangoes cost? (a) ₹67 (b) ₹147 (c) ₹441 (d) ₹168
40. 40.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days

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