Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 483 · 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.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹96 (b) ₹120 (c) ₹60 (d) ₹24
2. 2.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹60 (c) ₹70 (d) ₹10
3. 3.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 5 days (d) 45 days
4. 4.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 10 days (d) 3 days
5. 5.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹33 (d) ₹42
6. 6.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹470 (b) ₹188 (c) ₹423 (d) ₹47
7. 7.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹143 (c) ₹26 (d) ₹182
8. 8.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹1584 (b) ₹198 (c) ₹220 (d) ₹177
9. 9.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 27 days (d) 26 days
10. 10.If 2 mangoes cost ₹20, how much do 12 mangoes cost? (a) ₹120 (b) ₹240 (c) ₹30 (d) ₹130
11. 11.If 4 mangoes cost ₹72, how much do 8 mangoes cost? (a) ₹144 (b) ₹162 (c) ₹576 (d) ₹76
12. 12.If 8 pens cost ₹144, how much do 9 pens cost? (a) ₹180 (b) ₹145 (c) ₹1296 (d) ₹162
13. 13.If 2 mangoes cost ₹14, how much do 4 mangoes cost? (a) ₹56 (b) ₹16 (c) ₹28 (d) ₹35
14. 14.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹50 (d) ₹40
15. 15.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹64 (b) ₹56 (c) ₹16 (d) ₹48
16. 16.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 27 days
17. 17.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹264 (d) ₹288
18. 18.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹32 (b) ₹40 (c) ₹20 (d) ₹8
19. 19.If 7 notebooks cost ₹70, how much do 3 notebooks cost? (a) ₹210 (b) ₹40 (c) ₹30 (d) ₹66
20. 20.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 7 days (d) 8 days
21. 21.₹128 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹96 (d) ₹128
22. 22.If 2 pens cost ₹16, how much do 3 pens cost? (a) ₹24 (b) ₹32 (c) ₹17 (d) ₹48
23. 23.If 6 kites cost ₹150, how much do 4 kites cost? (a) ₹125 (b) ₹148 (c) ₹100 (d) ₹600
24. 24.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
25. 25.₹230 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹184 (b) ₹230 (c) ₹46 (d) ₹115
26. 26.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹42 (d) ₹56
27. 27.₹203 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹203 (b) ₹174 (c) ₹29 (d) ₹175
28. 28.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹13 (b) ₹60 (c) ₹15 (d) ₹18
29. 29.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 18 days (d) 11 days
30. 30.If 3 kites cost ₹54, how much do 12 kites cost? (a) ₹234 (b) ₹216 (c) ₹648 (d) ₹63
31. 31.If 8 mangoes cost ₹96, how much do 10 mangoes cost? (a) ₹960 (b) ₹120 (c) ₹132 (d) ₹98
32. 32.If 4 pens cost ₹24, how much do 8 pens cost? (a) ₹28 (b) ₹192 (c) ₹54 (d) ₹48
33. 33.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹209 (b) ₹190 (c) ₹228 (d) ₹38
34. 34.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹156 (d) ₹182
35. 35.If 7 pens cost ₹112, how much do 8 pens cost? (a) ₹128 (b) ₹896 (c) ₹113 (d) ₹144
36. 36.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹63 (b) ₹35 (c) ₹7 (d) ₹56
37. 37.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹36 (d) ₹30
38. 38.If 6 notebooks cost ₹18, how much do 4 notebooks cost? (a) ₹12 (b) ₹72 (c) ₹16 (d) ₹15
39. 39.₹252 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹216 (b) ₹126 (c) ₹36 (d) ₹252
40. 40.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹35 (b) ₹25 (c) ₹15 (d) ₹5

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