Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 785 · 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.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹40 (b) ₹240 (c) ₹280 (d) ₹140
2. 2.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 16 days (c) 21 days (d) 14 days
3. 3.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 9 days (d) 21 days
4. 4.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 4 days (d) 3 days
5. 5.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹44 (b) ₹198 (c) ₹88 (d) ₹308
6. 6.If 6 notebooks cost ₹108, how much do 7 notebooks cost? (a) ₹109 (b) ₹126 (c) ₹144 (d) ₹756
7. 7.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹43 (b) ₹387 (c) ₹430 (d) ₹172
8. 8.If 7 mangoes cost ₹147, how much do 11 mangoes cost? (a) ₹252 (b) ₹1617 (c) ₹231 (d) ₹151
9. 9.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹136 (b) ₹102 (c) ₹68 (d) ₹34
10. 10.If 5 notebooks cost ₹70, how much do 4 notebooks cost? (a) ₹70 (b) ₹56 (c) ₹69 (d) ₹280
11. 11.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹110 (d) ₹132
12. 12.₹215 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹43 (b) ₹86 (c) ₹129 (d) ₹172
13. 13.₹260 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹234 (b) ₹260 (c) ₹26 (d) ₹130
14. 14.If 8 notebooks cost ₹104, how much do 6 notebooks cost? (a) ₹91 (b) ₹78 (c) ₹102 (d) ₹624
15. 15.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹252 (c) ₹224 (d) ₹28
16. 16.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 21 days (c) 3 days (d) 48 days
17. 17.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹144 (b) ₹18 (c) ₹117 (d) ₹90
18. 18.If 4 pens cost ₹100, how much do 3 pens cost? (a) ₹75 (b) ₹99 (c) ₹100 (d) ₹300
19. 19.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 10 days (d) 9 days
20. 20.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹45 (b) ₹271 (c) ₹315 (d) ₹270
21. 21.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 1 day (d) 10 days
22. 22.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹273 (d) ₹195
23. 23.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹63 (d) ₹56
24. 24.If 4 mangoes cost ₹44, how much do 8 mangoes cost? (a) ₹88 (b) ₹99 (c) ₹352 (d) ₹48
25. 25.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹59 (d) ₹58
26. 26.If 3 kites cost ₹33, how much do 12 kites cost? (a) ₹42 (b) ₹396 (c) ₹143 (d) ₹132
27. 27.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹12 (b) ₹36 (c) ₹66 (d) ₹96
28. 28.If 4 pens cost ₹88, how much do 6 pens cost? (a) ₹528 (b) ₹90 (c) ₹154 (d) ₹132
29. 29.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹287 (c) ₹41 (d) ₹246
30. 30.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 30 days (d) 31 days
31. 31.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹126 (b) ₹56 (c) ₹28 (d) ₹196
32. 32.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹29 (b) ₹232 (c) ₹203 (d) ₹116
33. 33.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹80 (d) ₹10
34. 34.If 9 pens cost ₹171, how much do 4 pens cost? (a) ₹166 (b) ₹684 (c) ₹76 (d) ₹95
35. 35.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 29 days (d) 28 days
36. 36.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹162 (c) ₹99 (d) ₹36
37. 37.If 3 kites cost ₹15, how much do 11 kites cost? (a) ₹23 (b) ₹60 (c) ₹55 (d) ₹165
38. 38.If 2 kites cost ₹8, how much do 9 kites cost? (a) ₹40 (b) ₹72 (c) ₹15 (d) ₹36
39. 39.If 8 notebooks cost ₹104, how much do 7 notebooks cost? (a) ₹104 (b) ₹728 (c) ₹91 (d) ₹103
40. 40.If 2 mangoes cost ₹16, how much do 4 mangoes cost? (a) ₹40 (b) ₹32 (c) ₹64 (d) ₹18

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