Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 888 · 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. 1.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 12 days
2. 2.If 5 notebooks cost ₹55, how much do 8 notebooks cost? (a) ₹88 (b) ₹440 (c) ₹99 (d) ₹58
3. 3.If 7 notebooks cost ₹42, how much do 8 notebooks cost? (a) ₹48 (b) ₹43 (c) ₹54 (d) ₹336
4. 4.If 6 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹648 (b) ₹108 (c) ₹75 (d) ₹120
5. 5.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹85 (d) ₹51
6. 6.If 4 mangoes cost ₹52, how much do 5 mangoes cost? (a) ₹78 (b) ₹65 (c) ₹53 (d) ₹260
7. 7.If 9 kites cost ₹99, how much do 10 kites cost? (a) ₹100 (b) ₹121 (c) ₹990 (d) ₹110
8. 8.If 4 pens cost ₹84, how much do 10 pens cost? (a) ₹840 (b) ₹231 (c) ₹90 (d) ₹210
9. 9.If 4 kites cost ₹64, how much do 11 kites cost? (a) ₹71 (b) ₹704 (c) ₹192 (d) ₹176
10. 10.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹189 (b) ₹162 (c) ₹27 (d) ₹135
11. 11.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹400 (b) ₹325 (c) ₹250 (d) ₹50
12. 12.₹200 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹100 (b) ₹200 (c) ₹50 (d) ₹150
13. 13.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 7 days
14. 14.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 15 days (d) 7 days
15. 15.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹35 (d) ₹20
16. 16.If 8 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹10 (b) ₹80 (c) ₹34 (d) ₹15
17. 17.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 19 days
18. 18.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹67 (b) ₹99 (c) ₹33 (d) ₹66
19. 19.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹33 (b) ₹132 (c) ₹198 (d) ₹165
20. 20.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹76 (b) ₹266 (c) ₹38 (d) ₹171
21. 21.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹210 (c) ₹35 (d) ₹175
22. 22.If 6 mangoes cost ₹48, how much do 7 mangoes cost? (a) ₹64 (b) ₹336 (c) ₹49 (d) ₹56
23. 23.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹88 (b) ₹144 (c) ₹16 (d) ₹32
24. 24.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹343 (b) ₹245 (c) ₹294 (d) ₹49
25. 25.If 5 notebooks cost ₹105, how much do 9 notebooks cost? (a) ₹210 (b) ₹189 (c) ₹109 (d) ₹945
26. 26.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹25 (c) ₹10 (d) ₹50
27. 27.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹61 (b) ₹15 (c) ₹75 (d) ₹60
28. 28.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹55 (c) ₹11 (d) ₹44
29. 29.₹132 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹66 (b) ₹99 (c) ₹132 (d) ₹33
30. 30.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹144 (d) ₹54
31. 31.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 15 days (d) 6 days
32. 32.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 8 days (d) 6 days
33. 33.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 15 days (c) 8 days (d) 9 days
34. 34.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹187 (b) ₹34 (c) ₹170 (d) ₹204
35. 35.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 18 days (c) 8 days (d) 9 days
36. 36.₹385 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹245 (b) ₹280 (c) ₹35 (d) ₹140
37. 37.If 8 mangoes cost ₹168, how much do 9 mangoes cost? (a) ₹169 (b) ₹210 (c) ₹189 (d) ₹1512
38. 38.If 6 mangoes cost ₹132, how much do 9 mangoes cost? (a) ₹1188 (b) ₹135 (c) ₹198 (d) ₹220
39. 39.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹140 (c) ₹28 (d) ₹196
40. 40.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹60 (b) ₹70 (c) ₹35 (d) ₹10

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