Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 684 · 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 pens cost ₹24, how much do 9 pens cost? (a) ₹216 (b) ₹31 (c) ₹120 (d) ₹108
2. 2.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 12 days (d) 16 days
3. 3.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹129 (d) ₹172
4. 4.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹115 (b) ₹138 (c) ₹23 (d) ₹161
5. 5.If 2 kites cost ₹14, how much do 7 kites cost? (a) ₹98 (b) ₹19 (c) ₹49 (d) ₹56
6. 6.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 26 days (c) 17 days (d) 27 days
7. 7.If 6 kites cost ₹108, how much do 12 kites cost? (a) ₹234 (b) ₹216 (c) ₹1296 (d) ₹114
8. 8.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 1 day
9. 9.If 3 mangoes cost ₹66, how much do 2 mangoes cost? (a) ₹132 (b) ₹66 (c) ₹65 (d) ₹44
10. 10.If 4 pens cost ₹76, how much do 12 pens cost? (a) ₹84 (b) ₹247 (c) ₹228 (d) ₹912
11. 11.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹333 (d) ₹259
12. 12.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 15 days
13. 13.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 13 days
14. 14.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 6 days
15. 15.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 13 days (d) 9 days
16. 16.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 12 days (d) 9 days
17. 17.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹36 (d) ₹60
18. 18.₹56 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹35 (b) ₹21 (c) ₹7 (d) ₹28
19. 19.If 9 kites cost ₹216, how much do 7 kites cost? (a) ₹214 (b) ₹1512 (c) ₹168 (d) ₹192
20. 20.₹376 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹376 (d) ₹188
21. 21.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 9 days (c) 19 days (d) 4 days
22. 22.7 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
23. 23.₹264 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹216 (b) ₹48 (c) ₹132 (d) ₹24
24. 24.If 5 mangoes cost ₹70, how much do 8 mangoes cost? (a) ₹112 (b) ₹73 (c) ₹126 (d) ₹560
25. 25.If 5 kites cost ₹115, how much do 12 kites cost? (a) ₹276 (b) ₹122 (c) ₹1380 (d) ₹299
26. 26.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹10 (c) ₹30 (d) ₹40
27. 27.If 9 notebooks cost ₹36, how much do 10 notebooks cost? (a) ₹360 (b) ₹40 (c) ₹37 (d) ₹44
28. 28.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 19 days (d) 18 days
29. 29.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 20 days (c) 21 days (d) 5 days
30. 30.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹42 (d) ₹49
31. 31.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹63 (d) ₹72
32. 32.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 23 days (d) 22 days
33. 33.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹96 (c) ₹160 (d) ₹128
34. 34.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 10 days (d) 16 days
35. 35.If 7 notebooks cost ₹154, how much do 2 notebooks cost? (a) ₹308 (b) ₹44 (c) ₹149 (d) ₹66
36. 36.If 5 pens cost ₹80, how much do 10 pens cost? (a) ₹160 (b) ₹800 (c) ₹85 (d) ₹176
37. 37.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹170 (d) ₹153
38. 38.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹156 (d) ₹143
39. 39.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹62 (b) ₹248 (c) ₹217 (d) ₹31
40. 40.If 4 notebooks cost ₹88, how much do 7 notebooks cost? (a) ₹176 (b) ₹154 (c) ₹616 (d) ₹91

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