Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 299 · 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.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹138 (b) ₹139 (c) ₹23 (d) ₹161
2. 2.If 9 pens cost ₹99, how much do 2 pens cost? (a) ₹92 (b) ₹33 (c) ₹198 (d) ₹22
3. 3.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹116 (b) ₹145 (c) ₹29 (d) ₹87
4. 4.If 6 pens cost ₹72, how much do 12 pens cost? (a) ₹78 (b) ₹864 (c) ₹144 (d) ₹156
5. 5.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹126 (b) ₹36 (c) ₹108 (d) ₹144
6. 6.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 19 days (d) 11 days
7. 7.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 3 days (d) 6 days
8. 8.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹105 (d) ₹15
9. 9.If 8 pens cost ₹40, how much do 5 pens cost? (a) ₹37 (b) ₹30 (c) ₹200 (d) ₹25
10. 10.If 2 mangoes cost ₹50, how much do 9 mangoes cost? (a) ₹450 (b) ₹225 (c) ₹250 (d) ₹57
11. 11.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 6 days (d) 15 days
12. 12.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 13 days
13. 13.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 44 days (d) 5 days
14. 14.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹180 (b) ₹30 (c) ₹210 (d) ₹150
15. 15.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 18 days (d) 4 days
16. 16.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 18 days (d) 19 days
17. 17.If 9 notebooks cost ₹81, how much do 3 notebooks cost? (a) ₹243 (b) ₹36 (c) ₹75 (d) ₹27
18. 18.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 8 days (d) 9 days
19. 19.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 39 days (d) 7 days
20. 20.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 24 days (c) 6 days (d) 9 days
21. 21.If 3 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹180 (b) ₹24 (c) ₹65 (d) ₹60
22. 22.₹429 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹297 (b) ₹132 (c) ₹330 (d) ₹33
23. 23.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹210 (b) ₹84 (c) ₹189 (d) ₹21
24. 24.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 13 days
25. 25.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 30 days (d) 31 days
26. 26.If 2 pens cost ₹14, how much do 11 pens cost? (a) ₹84 (b) ₹77 (c) ₹23 (d) ₹154
27. 27.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 4 days (d) 3 days
28. 28.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹210 (b) ₹270 (c) ₹150 (d) ₹30
29. 29.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹31 (b) ₹62 (c) ₹124 (d) ₹93
30. 30.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 45 days (c) 5 days (d) 7 days
31. 31.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹85 (b) ₹102 (c) ₹119 (d) ₹17
32. 32.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 5 days (d) 45 days
33. 33.₹140 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹56 (c) ₹28 (d) ₹84
34. 34.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 29 days (d) 13 days
35. 35.If 9 notebooks cost ₹153, how much do 10 notebooks cost? (a) ₹170 (b) ₹154 (c) ₹1530 (d) ₹187
36. 36.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹105 (d) ₹126
37. 37.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹155 (b) ₹124 (c) ₹186 (d) ₹31
38. 38.If 2 kites cost ₹6, how much do 3 kites cost? (a) ₹9 (b) ₹12 (c) ₹18 (d) ₹7
39. 39.If 3 pens cost ₹57, how much do 8 pens cost? (a) ₹62 (b) ₹171 (c) ₹152 (d) ₹456
40. 40.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 10 days (d) 9 days

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