Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 257 · 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.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹6 (c) ₹18 (d) ₹9
2. 2.If 2 pens cost ₹8, how much do 11 pens cost? (a) ₹17 (b) ₹48 (c) ₹88 (d) ₹44
3. 3.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 15 days (c) 1 day (d) 36 days
4. 4.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹80 (d) ₹65
5. 5.If 7 kites cost ₹91, how much do 10 kites cost? (a) ₹94 (b) ₹130 (c) ₹143 (d) ₹910
6. 6.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 4 days (d) 3 days
7. 7.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 25 days (c) 2 days (d) 24 days
8. 8.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹98 (b) ₹140 (c) ₹56 (d) ₹28
9. 9.₹155 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹155 (d) ₹125
10. 10.If 4 pens cost ₹52, how much do 9 pens cost? (a) ₹130 (b) ₹468 (c) ₹117 (d) ₹57
11. 11.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 32 days (d) 33 days
12. 12.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 14 days
13. 13.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 9 days (d) 12 days
14. 14.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹26 (c) ₹169 (d) ₹104
15. 15.If 4 kites cost ₹96, how much do 6 kites cost? (a) ₹144 (b) ₹576 (c) ₹168 (d) ₹98
16. 16.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 9 days
17. 17.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹86 (b) ₹87 (c) ₹43 (d) ₹129
18. 18.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 24 days (c) 16 days (d) 6 days
19. 19.If 7 pens cost ₹77, how much do 8 pens cost? (a) ₹88 (b) ₹616 (c) ₹99 (d) ₹78
20. 20.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 11 days (d) 3 days
21. 21.If 7 kites cost ₹98, how much do 3 kites cost? (a) ₹56 (b) ₹94 (c) ₹294 (d) ₹42
22. 22.If 7 notebooks cost ₹49, how much do 6 notebooks cost? (a) ₹49 (b) ₹48 (c) ₹42 (d) ₹294
23. 23.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹39 (b) ₹24 (c) ₹6 (d) ₹54
24. 24.If 6 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹132 (b) ₹720 (c) ₹76 (d) ₹120
25. 25.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 15 days (d) 5 days
26. 26.If 3 notebooks cost ₹60, how much do 12 notebooks cost? (a) ₹720 (b) ₹240 (c) ₹260 (d) ₹69
27. 27.If 3 mangoes cost ₹54, how much do 9 mangoes cost? (a) ₹486 (b) ₹60 (c) ₹180 (d) ₹162
28. 28.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 15 days (d) 9 days
29. 29.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 4 days (d) 25 days
30. 30.If 9 kites cost ₹108, how much do 10 kites cost? (a) ₹1080 (b) ₹132 (c) ₹109 (d) ₹120
31. 31.₹240 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹240 (b) ₹120 (c) ₹210 (d) ₹30
32. 32.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 12 days (d) 3 days
33. 33.If 6 pens cost ₹114, how much do 8 pens cost? (a) ₹171 (b) ₹116 (c) ₹912 (d) ₹152
34. 34.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 13 days
35. 35.If 6 notebooks cost ₹102, how much do 10 notebooks cost? (a) ₹170 (b) ₹1020 (c) ₹106 (d) ₹187
36. 36.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹119 (d) ₹68
37. 37.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 7 days (d) 6 days
38. 38.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 12 days (d) 10 days
39. 39.If 7 mangoes cost ₹49, how much do 6 mangoes cost? (a) ₹42 (b) ₹48 (c) ₹49 (d) ₹294
40. 40.If 7 notebooks cost ₹119, how much do 9 notebooks cost? (a) ₹153 (b) ₹1071 (c) ₹121 (d) ₹170

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