Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 537 · 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 7 kites cost ₹126, how much do 3 kites cost? (a) ₹54 (b) ₹72 (c) ₹378 (d) ₹122
2. 2.If 8 pens cost ₹128, how much do 9 pens cost? (a) ₹1152 (b) ₹160 (c) ₹129 (d) ₹144
3. 3.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 19 days (d) 39 days
4. 4.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹102 (d) ₹85
5. 5.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 7 days (d) 8 days
6. 6.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹16 (b) ₹72 (c) ₹112 (d) ₹32
7. 7.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹65 (c) ₹13 (d) ₹52
8. 8.If 2 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹324 (b) ₹180 (c) ₹43 (d) ₹162
9. 9.If 5 notebooks cost ₹85, how much do 6 notebooks cost? (a) ₹119 (b) ₹102 (c) ₹510 (d) ₹86
10. 10.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 11 days (d) 12 days
11. 11.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 6 days
12. 12.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹384 (d) ₹312
13. 13.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹156 (b) ₹117 (c) ₹39 (d) ₹195
14. 14.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹90 (c) ₹54 (d) ₹18
15. 15.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 24 days (d) 17 days
16. 16.If 7 pens cost ₹42, how much do 5 pens cost? (a) ₹36 (b) ₹30 (c) ₹40 (d) ₹210
17. 17.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹16 (b) ₹36 (c) ₹56 (d) ₹8
18. 18.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 27 days (d) 3 days
19. 19.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 15 days (d) 16 days
20. 20.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹32 (d) ₹24
21. 21.If 8 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹38 (b) ₹240 (c) ₹35 (d) ₹30
22. 22.5 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
23. 23.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹84 (b) ₹210 (c) ₹189 (d) ₹21
24. 24.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 8 days (d) 4 days
25. 25.If 5 notebooks cost ₹45, how much do 6 notebooks cost? (a) ₹54 (b) ₹270 (c) ₹46 (d) ₹63
26. 26.₹63 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹55 (b) ₹9 (c) ₹54 (d) ₹63
27. 27.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹65 (d) ₹91
28. 28.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹46 (b) ₹414 (c) ₹184 (d) ₹299
29. 29.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹45 (d) ₹40
30. 30.If 7 kites cost ₹126, how much do 9 kites cost? (a) ₹180 (b) ₹162 (c) ₹1134 (d) ₹128
31. 31.If 7 notebooks cost ₹126, how much do 6 notebooks cost? (a) ₹756 (b) ₹126 (c) ₹108 (d) ₹125
32. 32.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹207 (d) ₹230
33. 33.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹58 (b) ₹87 (c) ₹29 (d) ₹116
34. 34.If 5 mangoes cost ₹100, how much do 7 mangoes cost? (a) ₹700 (b) ₹102 (c) ₹160 (d) ₹140
35. 35.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
36. 36.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹8 (b) ₹64 (c) ₹24 (d) ₹44
37. 37.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹21 (c) ₹28 (d) ₹7
38. 38.If 3 pens cost ₹24, how much do 4 pens cost? (a) ₹32 (b) ₹25 (c) ₹40 (d) ₹96
39. 39.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 4 days (d) 5 days
40. 40.If 8 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹90 (b) ₹648 (c) ₹81 (d) ₹73

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