Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 106 · 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 4 pens cost ₹92, how much do 10 pens cost? (a) ₹920 (b) ₹253 (c) ₹98 (d) ₹230
2. 2.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
3. 3.If 5 mangoes cost ₹120, how much do 11 mangoes cost? (a) ₹288 (b) ₹126 (c) ₹264 (d) ₹1320
4. 4.If 6 notebooks cost ₹96, how much do 10 notebooks cost? (a) ₹100 (b) ₹176 (c) ₹160 (d) ₹960
5. 5.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 10 days (d) 9 days
6. 6.₹56 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹28 (c) ₹7 (d) ₹35
7. 7.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 17 days (c) 33 days (d) 7 days
8. 8.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 6 days (d) 7 days
9. 9.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹132 (b) ₹33 (c) ₹198 (d) ₹165
10. 10.₹42 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹6 (b) ₹21 (c) ₹36 (d) ₹42
11. 11.If 7 notebooks cost ₹63, how much do 8 notebooks cost? (a) ₹504 (b) ₹64 (c) ₹81 (d) ₹72
12. 12.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹360 (b) ₹40 (c) ₹260 (d) ₹160
13. 13.If 9 kites cost ₹99, how much do 6 kites cost? (a) ₹66 (b) ₹77 (c) ₹594 (d) ₹96
14. 14.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹29 (b) ₹290 (c) ₹261 (d) ₹145
15. 15.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹40 (c) ₹5 (d) ₹25
16. 16.If 3 pens cost ₹21, how much do 7 pens cost? (a) ₹49 (b) ₹56 (c) ₹147 (d) ₹25
17. 17.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹252 (b) ₹42 (c) ₹294 (d) ₹210
18. 18.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹140 (b) ₹105 (c) ₹35 (d) ₹70
19. 19.If 4 pens cost ₹80, how much do 2 pens cost? (a) ₹40 (b) ₹160 (c) ₹78 (d) ₹60
20. 20.If 3 mangoes cost ₹57, how much do 6 mangoes cost? (a) ₹114 (b) ₹342 (c) ₹60 (d) ₹133
21. 21.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 37 days (c) 36 days (d) 15 days
22. 22.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹42 (b) ₹168 (c) ₹126 (d) ₹210
23. 23.If 2 mangoes cost ₹8, how much do 9 mangoes cost? (a) ₹40 (b) ₹36 (c) ₹72 (d) ₹15
24. 24.₹430 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹215 (b) ₹301 (c) ₹129 (d) ₹43
25. 25.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹50 (c) ₹25 (d) ₹10
26. 26.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹27 (b) ₹270 (c) ₹108 (d) ₹243
27. 27.If 4 notebooks cost ₹40, how much do 5 notebooks cost? (a) ₹200 (b) ₹60 (c) ₹41 (d) ₹50
28. 28.If 5 mangoes cost ₹115, how much do 3 mangoes cost? (a) ₹92 (b) ₹345 (c) ₹69 (d) ₹113
29. 29.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹165 (b) ₹297 (c) ₹33 (d) ₹264
30. 30.If 4 kites cost ₹76, how much do 5 kites cost? (a) ₹95 (b) ₹380 (c) ₹114 (d) ₹77
31. 31.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹74 (b) ₹37 (c) ₹148 (d) ₹111
32. 32.If 9 mangoes cost ₹54, how much do 7 mangoes cost? (a) ₹52 (b) ₹42 (c) ₹48 (d) ₹378
33. 33.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 2 days
34. 34.If 8 pens cost ₹200, how much do 7 pens cost? (a) ₹200 (b) ₹175 (c) ₹199 (d) ₹1400
35. 35.If 6 kites cost ₹24, how much do 5 kites cost? (a) ₹24 (b) ₹120 (c) ₹20 (d) ₹23
36. 36.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 16 days (d) 3 days
37. 37.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 13 days (d) 21 days
38. 38.If 4 notebooks cost ₹88, how much do 2 notebooks cost? (a) ₹176 (b) ₹86 (c) ₹44 (d) ₹66
39. 39.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 19 days (c) 4 days (d) 6 days
40. 40.If 2 kites cost ₹12, how much do 8 kites cost? (a) ₹48 (b) ₹18 (c) ₹54 (d) ₹96

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