Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 215 · 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 5 notebooks cost ₹45, how much do 7 notebooks cost? (a) ₹47 (b) ₹63 (c) ₹72 (d) ₹315
2. 2.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 2 days
3. 3.If 4 pens cost ₹84, how much do 5 pens cost? (a) ₹105 (b) ₹126 (c) ₹85 (d) ₹420
4. 4.If 9 pens cost ₹207, how much do 10 pens cost? (a) ₹2070 (b) ₹208 (c) ₹253 (d) ₹230
5. 5.If 4 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹13 (b) ₹18 (c) ₹15 (d) ₹60
6. 6.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 15 days (d) 20 days
7. 7.If 4 pens cost ₹100, how much do 11 pens cost? (a) ₹300 (b) ₹1100 (c) ₹107 (d) ₹275
8. 8.If 4 kites cost ₹16, how much do 3 kites cost? (a) ₹15 (b) ₹48 (c) ₹12 (d) ₹16
9. 9.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 14 days (d) 15 days
10. 10.If 5 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹180 (b) ₹36 (c) ₹39 (d) ₹22
11. 11.4 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
12. 12.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹60 (d) ₹75
13. 13.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹176 (b) ₹22 (c) ₹121 (d) ₹66
14. 14.If 3 pens cost ₹48, how much do 8 pens cost? (a) ₹53 (b) ₹128 (c) ₹384 (d) ₹144
15. 15.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹54 (b) ₹27 (c) ₹189 (d) ₹216
16. 16.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹221 (b) ₹170 (c) ₹272 (d) ₹34
17. 17.If 3 pens cost ₹27, how much do 7 pens cost? (a) ₹189 (b) ₹31 (c) ₹72 (d) ₹63
18. 18.If 3 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹40 (b) ₹50 (c) ₹120 (d) ₹31
19. 19.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 33 days (d) 32 days
20. 20.₹297 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹265 (b) ₹297 (c) ₹264 (d) ₹33
21. 21.If 8 mangoes cost ₹112, how much do 10 mangoes cost? (a) ₹154 (b) ₹114 (c) ₹1120 (d) ₹140
22. 22.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹116 (d) ₹58
23. 23.If 7 notebooks cost ₹91, how much do 10 notebooks cost? (a) ₹910 (b) ₹130 (c) ₹143 (d) ₹94
24. 24.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 11 days (d) 26 days
25. 25.If 3 kites cost ₹9, how much do 5 kites cost? (a) ₹18 (b) ₹11 (c) ₹15 (d) ₹45
26. 26.If 9 pens cost ₹72, how much do 6 pens cost? (a) ₹69 (b) ₹56 (c) ₹48 (d) ₹432
27. 27.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹38 (b) ₹152 (c) ₹190 (d) ₹171
28. 28.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹21 (c) ₹63 (d) ₹42
29. 29.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 22 days (d) 13 days
30. 30.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹119 (b) ₹136 (c) ₹68 (d) ₹17
31. 31.₹250 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹125 (d) ₹150
32. 32.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹64 (d) ₹52
33. 33.If 7 mangoes cost ₹105, how much do 4 mangoes cost? (a) ₹420 (b) ₹60 (c) ₹102 (d) ₹75
34. 34.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 53 days (d) 52 days
35. 35.₹140 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹70 (b) ₹28 (c) ₹140 (d) ₹112
36. 36.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹196 (d) ₹147
37. 37.If 7 pens cost ₹147, how much do 4 pens cost? (a) ₹588 (b) ₹144 (c) ₹105 (d) ₹84
38. 38.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹111 (b) ₹148 (c) ₹37 (d) ₹185
39. 39.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
40. 40.If 6 notebooks cost ₹54, how much do 11 notebooks cost? (a) ₹594 (b) ₹99 (c) ₹108 (d) ₹59

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