Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 811 · 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. 1.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 7 days (d) 33 days
2. 2.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 2 days (d) 8 days
3. 3.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹55 (c) ₹27 (d) ₹81
4. 4.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 49 days (d) 19 days
5. 5.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹36 (d) ₹24
6. 6.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 2 days (d) 3 days
7. 7.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹49 (b) ₹35 (c) ₹42 (d) ₹7
8. 8.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹231 (b) ₹264 (c) ₹132 (d) ₹33
9. 9.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹360 (b) ₹200 (c) ₹40 (d) ₹400
10. 10.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 63 days (c) 7 days (d) 21 days
11. 11.If 7 kites cost ₹21, how much do 8 kites cost? (a) ₹22 (b) ₹27 (c) ₹24 (d) ₹168
12. 12.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day
13. 13.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹78 (c) ₹79 (d) ₹13
14. 14.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 13 days (d) 12 days
15. 15.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 11 days (d) 4 days
16. 16.If 4 pens cost ₹80, how much do 11 pens cost? (a) ₹220 (b) ₹880 (c) ₹87 (d) ₹240
17. 17.If 4 mangoes cost ₹64, how much do 5 mangoes cost? (a) ₹65 (b) ₹80 (c) ₹320 (d) ₹96
18. 18.If 8 notebooks cost ₹176, how much do 6 notebooks cost? (a) ₹1056 (b) ₹174 (c) ₹154 (d) ₹132
19. 19.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 1 day
20. 20.If 4 kites cost ₹20, how much do 5 kites cost? (a) ₹30 (b) ₹21 (c) ₹100 (d) ₹25
21. 21.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹37 (b) ₹259 (c) ₹223 (d) ₹222
22. 22.If 5 notebooks cost ₹125, how much do 7 notebooks cost? (a) ₹200 (b) ₹875 (c) ₹175 (d) ₹127
23. 23.If 2 pens cost ₹14, how much do 9 pens cost? (a) ₹21 (b) ₹63 (c) ₹70 (d) ₹126
24. 24.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹110 (b) ₹11 (c) ₹99 (d) ₹22
25. 25.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 7 days (d) 8 days
26. 26.If 8 kites cost ₹144, how much do 10 kites cost? (a) ₹146 (b) ₹1440 (c) ₹180 (d) ₹198
27. 27.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 8 days (d) 18 days
28. 28.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹138 (b) ₹115 (c) ₹161 (d) ₹23
29. 29.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 9 days (d) 17 days
30. 30.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹168 (d) ₹126
31. 31.If 9 notebooks cost ₹81, how much do 11 notebooks cost? (a) ₹99 (b) ₹83 (c) ₹108 (d) ₹891
32. 32.6 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) 22 days (d) 21 days
33. 33.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹80 (c) ₹10 (d) ₹45
34. 34.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 31 days (d) 30 days
35. 35.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹230 (b) ₹184 (c) ₹207 (d) ₹46
36. 36.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹15 (c) ₹75 (d) ₹30
37. 37.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 9 days (d) 10 days
38. 38.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹90 (d) ₹81
39. 39.If 2 mangoes cost ₹26, how much do 10 mangoes cost? (a) ₹260 (b) ₹130 (c) ₹143 (d) ₹34
40. 40.If 5 notebooks cost ₹70, how much do 4 notebooks cost? (a) ₹56 (b) ₹280 (c) ₹70 (d) ₹69

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