Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 825 · 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 ₹12, how much do 11 pens cost? (a) ₹72 (b) ₹132 (c) ₹21 (d) ₹66
2. 2.If 9 pens cost ₹225, how much do 3 pens cost? (a) ₹75 (b) ₹219 (c) ₹675 (d) ₹100
3. 3.₹516 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹301 (b) ₹43 (c) ₹215 (d) ₹258
4. 4.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹280 (d) ₹120
5. 5.If 3 notebooks cost ₹12, how much do 10 notebooks cost? (a) ₹40 (b) ₹120 (c) ₹19 (d) ₹44
6. 6.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 14 days (d) 11 days
7. 7.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹130 (b) ₹208 (c) ₹26 (d) ₹169
8. 8.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 8 days
9. 9.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹20 (b) ₹180 (c) ₹140 (d) ₹100
10. 10.8 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) 7 days (d) 14 days
11. 11.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹141 (b) ₹329 (c) ₹47 (d) ₹235
12. 12.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 33 days (c) 7 days (d) 34 days
13. 13.If 9 kites cost ₹54, how much do 6 kites cost? (a) ₹42 (b) ₹36 (c) ₹324 (d) ₹51
14. 14.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹154 (b) ₹88 (c) ₹220 (d) ₹44
15. 15.If 2 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹37 (b) ₹112 (c) ₹128 (d) ₹224
16. 16.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
17. 17.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹25 (d) ₹15
18. 18.If 5 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹41 (b) ₹48 (c) ₹56 (d) ₹240
19. 19.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹91 (b) ₹78 (c) ₹13 (d) ₹65
20. 20.If 3 pens cost ₹45, how much do 9 pens cost? (a) ₹150 (b) ₹405 (c) ₹51 (d) ₹135
21. 21.If 6 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹144 (b) ₹27 (c) ₹24 (d) ₹20
22. 22.If 6 mangoes cost ₹90, how much do 3 mangoes cost? (a) ₹45 (b) ₹270 (c) ₹60 (d) ₹87
23. 23.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹70 (b) ₹280 (c) ₹35 (d) ₹245
24. 24.If 2 pens cost ₹50, how much do 3 pens cost? (a) ₹75 (b) ₹150 (c) ₹100 (d) ₹51
25. 25.₹152 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹152 (c) ₹38 (d) ₹114
26. 26.If 3 pens cost ₹12, how much do 2 pens cost? (a) ₹12 (b) ₹24 (c) ₹11 (d) ₹8
27. 27.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 11 days (d) 8 days
28. 28.If 6 mangoes cost ₹66, how much do 7 mangoes cost? (a) ₹67 (b) ₹462 (c) ₹88 (d) ₹77
29. 29.If 4 notebooks cost ₹60, how much do 6 notebooks cost? (a) ₹62 (b) ₹360 (c) ₹90 (d) ₹105
30. 30.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹42 (b) ₹336 (c) ₹168 (d) ₹294
31. 31.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 11 days (d) 16 days
32. 32.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹174 (d) ₹145
33. 33.7 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
34. 34.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 46 days (b) 45 days (c) 3 days (d) 17 days
35. 35.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 17 days
36. 36.If 2 mangoes cost ₹14, how much do 10 mangoes cost? (a) ₹70 (b) ₹140 (c) ₹22 (d) ₹77
37. 37.If 9 pens cost ₹117, how much do 11 pens cost? (a) ₹1287 (b) ₹143 (c) ₹156 (d) ₹119
38. 38.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹75 (d) ₹90
39. 39.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹14 (d) ₹21
40. 40.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 17 days (c) 32 days (d) 7 days

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