Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 845 · 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. 1.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 23 days (c) 12 days (d) 24 days
2. 2.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹92 (b) ₹69 (c) ₹23 (d) ₹46
3. 3.₹385 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹315 (b) ₹35 (c) ₹105 (d) ₹280
4. 4.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 25 days (c) 24 days (d) 14 days
5. 5.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹98 (b) ₹70 (c) ₹84 (d) ₹14
6. 6.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
7. 7.If 8 notebooks cost ₹104, how much do 9 notebooks cost? (a) ₹105 (b) ₹936 (c) ₹130 (d) ₹117
8. 8.If 6 pens cost ₹60, how much do 7 pens cost? (a) ₹80 (b) ₹420 (c) ₹70 (d) ₹61
9. 9.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 17 days (d) 3 days
10. 10.If 4 notebooks cost ₹100, how much do 2 notebooks cost? (a) ₹50 (b) ₹200 (c) ₹98 (d) ₹75
11. 11.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 8 days (d) 13 days
12. 12.If 7 notebooks cost ₹49, how much do 6 notebooks cost? (a) ₹48 (b) ₹294 (c) ₹49 (d) ₹42
13. 13.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹130 (b) ₹78 (c) ₹182 (d) ₹26
14. 14.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 6 days (d) 7 days
15. 15.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 3 days (d) 12 days
16. 16.If 6 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹28 (b) ₹44 (c) ₹240 (d) ₹40
17. 17.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹243 (b) ₹216 (c) ₹27 (d) ₹217
18. 18.If 7 notebooks cost ₹119, how much do 9 notebooks cost? (a) ₹1071 (b) ₹170 (c) ₹153 (d) ₹121
19. 19.If 7 pens cost ₹56, how much do 3 pens cost? (a) ₹168 (b) ₹24 (c) ₹52 (d) ₹32
20. 20.If 5 mangoes cost ₹95, how much do 8 mangoes cost? (a) ₹760 (b) ₹171 (c) ₹152 (d) ₹98
21. 21.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹152 (b) ₹19 (c) ₹171 (d) ₹95
22. 22.If 3 pens cost ₹66, how much do 7 pens cost? (a) ₹176 (b) ₹70 (c) ₹154 (d) ₹462
23. 23.If 2 pens cost ₹18, how much do 6 pens cost? (a) ₹54 (b) ₹63 (c) ₹22 (d) ₹108
24. 24.If 8 pens cost ₹88, how much do 6 pens cost? (a) ₹77 (b) ₹528 (c) ₹66 (d) ₹86
25. 25.If 5 notebooks cost ₹75, how much do 6 notebooks cost? (a) ₹105 (b) ₹90 (c) ₹450 (d) ₹76
26. 26.If 4 pens cost ₹32, how much do 6 pens cost? (a) ₹56 (b) ₹48 (c) ₹192 (d) ₹34
27. 27.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 23 days (d) 9 days
28. 28.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 3 days (d) 2 days
29. 29.If 3 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹120 (b) ₹31 (c) ₹50 (d) ₹40
30. 30.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 10 days (d) 16 days
31. 31.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 10 days (d) 16 days
32. 32.If 2 notebooks cost ₹14, how much do 3 notebooks cost? (a) ₹28 (b) ₹21 (c) ₹15 (d) ₹42
33. 33.If 3 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹56 (b) ₹70 (c) ₹43 (d) ₹168
34. 34.If 4 pens cost ₹36, how much do 9 pens cost? (a) ₹90 (b) ₹324 (c) ₹81 (d) ₹41
35. 35.If 3 pens cost ₹24, how much do 2 pens cost? (a) ₹48 (b) ₹23 (c) ₹16 (d) ₹24
36. 36.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 10 days (d) 9 days
37. 37.If 5 pens cost ₹40, how much do 12 pens cost? (a) ₹47 (b) ₹480 (c) ₹96 (d) ₹104
38. 38.If 8 pens cost ₹104, how much do 5 pens cost? (a) ₹101 (b) ₹65 (c) ₹520 (d) ₹78
39. 39.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
40. 40.₹133 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹133 (b) ₹114 (c) ₹19 (d) ₹115

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