Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 604 · 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.₹294 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹42 (b) ₹168 (c) ₹147 (d) ₹126
2. 2.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹33 (b) ₹133 (c) ₹132 (d) ₹165
3. 3.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹60 (b) ₹75 (c) ₹15 (d) ₹61
4. 4.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 3 days (d) 12 days
5. 5.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 11 days (d) 14 days
6. 6.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹44 (d) ₹48
7. 7.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 15 days (d) 10 days
8. 8.If 3 pens cost ₹69, how much do 5 pens cost? (a) ₹71 (b) ₹138 (c) ₹115 (d) ₹345
9. 9.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 13 days (d) 7 days
10. 10.If 9 kites cost ₹117, how much do 10 kites cost? (a) ₹143 (b) ₹1170 (c) ₹118 (d) ₹130
11. 11.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 15 days (d) 5 days
12. 12.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 17 days (d) 7 days
13. 13.If 5 notebooks cost ₹80, how much do 12 notebooks cost? (a) ₹960 (b) ₹208 (c) ₹192 (d) ₹87
14. 14.If 3 mangoes cost ₹75, how much do 11 mangoes cost? (a) ₹275 (b) ₹300 (c) ₹83 (d) ₹825
15. 15.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 11 days (d) 3 days
16. 16.If 3 pens cost ₹36, how much do 4 pens cost? (a) ₹60 (b) ₹37 (c) ₹48 (d) ₹144
17. 17.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹168 (b) ₹210 (c) ₹42 (d) ₹105
18. 18.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 19 days
19. 19.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 3 days (d) 2 days
20. 20.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹225 (b) ₹25 (c) ₹125 (d) ₹200
21. 21.₹128 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹48 (b) ₹80 (c) ₹16 (d) ₹64
22. 22.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 26 days (d) 27 days
23. 23.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹99 (b) ₹72 (c) ₹18 (d) ₹126
24. 24.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 16 days (d) 5 days
25. 25.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹36 (c) ₹324 (d) ₹144
26. 26.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹55 (b) ₹66 (c) ₹11 (d) ₹77
27. 27.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
28. 28.If 8 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹60 (b) ₹49 (c) ₹432 (d) ₹54
29. 29.If 4 pens cost ₹80, how much do 12 pens cost? (a) ₹960 (b) ₹260 (c) ₹240 (d) ₹88
30. 30.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹75 (c) ₹30 (d) ₹90
31. 31.₹210 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹210 (d) ₹189
32. 32.If 6 pens cost ₹42, how much do 7 pens cost? (a) ₹294 (b) ₹43 (c) ₹49 (d) ₹56
33. 33.If 5 kites cost ₹50, how much do 6 kites cost? (a) ₹51 (b) ₹70 (c) ₹300 (d) ₹60
34. 34.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹189 (d) ₹27
35. 35.If 3 pens cost ₹66, how much do 11 pens cost? (a) ₹74 (b) ₹242 (c) ₹264 (d) ₹726
36. 36.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹48 (b) ₹13 (c) ₹16 (d) ₹20
37. 37.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 4 days (d) 15 days
38. 38.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 5 days (d) 4 days
39. 39.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹34 (d) ₹51
40. 40.If 6 pens cost ₹48, how much do 10 pens cost? (a) ₹480 (b) ₹52 (c) ₹88 (d) ₹80

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