Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 33 · 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 3 pens cost ₹54, how much do 7 pens cost? (a) ₹144 (b) ₹378 (c) ₹58 (d) ₹126
2. 2.If 7 mangoes cost ₹105, how much do 5 mangoes cost? (a) ₹525 (b) ₹103 (c) ₹90 (d) ₹75
3. 3.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 6 days (d) 5 days
4. 4.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹234 (b) ₹36 (c) ₹288 (d) ₹180
5. 5.If 3 pens cost ₹18, how much do 5 pens cost? (a) ₹30 (b) ₹90 (c) ₹36 (d) ₹20
6. 6.If 2 kites cost ₹26, how much do 3 kites cost? (a) ₹78 (b) ₹39 (c) ₹52 (d) ₹27
7. 7.If 3 kites cost ₹27, how much do 4 kites cost? (a) ₹36 (b) ₹28 (c) ₹108 (d) ₹45
8. 8.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹136 (d) ₹119
9. 9.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 16 days (d) 10 days
10. 10.If 3 kites cost ₹42, how much do 6 kites cost? (a) ₹98 (b) ₹252 (c) ₹84 (d) ₹45
11. 11.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 11 days (d) 28 days
12. 12.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹336 (b) ₹216 (c) ₹48 (d) ₹96
13. 13.₹168 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹140 (b) ₹168 (c) ₹84 (d) ₹28
14. 14.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹25 (d) ₹225
15. 15.If 6 notebooks cost ₹144, how much do 7 notebooks cost? (a) ₹192 (b) ₹168 (c) ₹145 (d) ₹1008
16. 16.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹11 (d) ₹77
17. 17.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 8 days (d) 2 days
18. 18.If 8 pens cost ₹112, how much do 11 pens cost? (a) ₹168 (b) ₹115 (c) ₹1232 (d) ₹154
19. 19.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 3 days (d) 2 days
20. 20.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 15 days (d) 22 days
21. 21.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹50 (d) ₹45
22. 22.If 2 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹120 (b) ₹80 (c) ₹60 (d) ₹41
23. 23.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹180 (d) ₹110
24. 24.₹51 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹34 (c) ₹17 (d) ₹35
25. 25.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 11 days (c) 17 days (d) 35 days
26. 26.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹27 (d) ₹45
27. 27.If 8 kites cost ₹192, how much do 2 kites cost? (a) ₹48 (b) ₹384 (c) ₹72 (d) ₹186
28. 28.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 11 days (d) 16 days
29. 29.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 17 days (d) 6 days
30. 30.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 14 days (c) 32 days (d) 2 days
31. 31.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹136 (d) ₹34
32. 32.If 3 mangoes cost ₹60, how much do 9 mangoes cost? (a) ₹540 (b) ₹180 (c) ₹200 (d) ₹66
33. 33.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 1 day (d) 7 days
34. 34.If 9 mangoes cost ₹189, how much do 3 mangoes cost? (a) ₹84 (b) ₹63 (c) ₹183 (d) ₹567
35. 35.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 5 days
36. 36.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹203 (b) ₹87 (c) ₹29 (d) ₹145
37. 37.If 3 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹648 (b) ₹240 (c) ₹78 (d) ₹216
38. 38.₹81 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹63 (d) ₹72
39. 39.If 2 mangoes cost ₹38, how much do 5 mangoes cost? (a) ₹95 (b) ₹114 (c) ₹190 (d) ₹41
40. 40.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 13 days (d) 12 days

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