Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 621 · 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 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 7 days
2. 2.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹147 (d) ₹196
3. 3.If 9 pens cost ₹189, how much do 3 pens cost? (a) ₹567 (b) ₹183 (c) ₹84 (d) ₹63
4. 4.If 6 mangoes cost ₹60, how much do 3 mangoes cost? (a) ₹40 (b) ₹180 (c) ₹30 (d) ₹57
5. 5.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 45 days (d) 21 days
6. 6.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 3 days (d) 5 days
7. 7.If 2 notebooks cost ₹6, how much do 9 notebooks cost? (a) ₹30 (b) ₹27 (c) ₹54 (d) ₹13
8. 8.If 9 pens cost ₹207, how much do 6 pens cost? (a) ₹1242 (b) ₹161 (c) ₹204 (d) ₹138
9. 9.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 13 days (d) 1 day
10. 10.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 5 days (c) 4 days (d) 3 days
11. 11.If 6 pens cost ₹96, how much do 3 pens cost? (a) ₹288 (b) ₹64 (c) ₹48 (d) ₹93
12. 12.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 5 days (d) 20 days
13. 13.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹133 (b) ₹95 (c) ₹114 (d) ₹19
14. 14.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 24 days (b) 15 days (c) 6 days (d) 9 days
15. 15.If 8 pens cost ₹128, how much do 11 pens cost? (a) ₹176 (b) ₹131 (c) ₹192 (d) ₹1408
16. 16.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 18 days (c) 43 days (d) 10 days
17. 17.If 8 pens cost ₹104, how much do 7 pens cost? (a) ₹104 (b) ₹91 (c) ₹728 (d) ₹103
18. 18.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹115 (d) ₹92
19. 19.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
20. 20.If 2 mangoes cost ₹8, how much do 4 mangoes cost? (a) ₹20 (b) ₹10 (c) ₹16 (d) ₹32
21. 21.If 6 notebooks cost ₹102, how much do 10 notebooks cost? (a) ₹106 (b) ₹170 (c) ₹1020 (d) ₹187
22. 22.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹72 (c) ₹12 (d) ₹84
23. 23.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹165 (b) ₹133 (c) ₹132 (d) ₹33
24. 24.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 9 days (d) 12 days
25. 25.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹245 (b) ₹441 (c) ₹49 (d) ₹490
26. 26.If 8 pens cost ₹200, how much do 10 pens cost? (a) ₹202 (b) ₹250 (c) ₹275 (d) ₹2000
27. 27.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹38 (b) ₹266 (c) ₹228 (d) ₹190
28. 28.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 14 days (d) 10 days
29. 29.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 16 days (d) 8 days
30. 30.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 9 days (d) 10 days
31. 31.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹182 (b) ₹28 (c) ₹252 (d) ₹112
32. 32.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹174 (b) ₹145 (c) ₹29 (d) ₹58
33. 33.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
34. 34.9 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) 7 days (d) 39 days
35. 35.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹161 (b) ₹230 (c) ₹92 (d) ₹46
36. 36.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 10 days
37. 37.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹12 (b) ₹108 (c) ₹78 (d) ₹48
38. 38.If 7 kites cost ₹147, how much do 3 kites cost? (a) ₹143 (b) ₹441 (c) ₹84 (d) ₹63
39. 39.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹231 (b) ₹165 (c) ₹297 (d) ₹33
40. 40.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹208 (b) ₹256 (c) ₹32 (d) ₹160

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