Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 291 · 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 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 32 days (c) 2 days (d) 33 days
2. 2.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 7 days
3. 3.If 2 pens cost ₹8, how much do 5 pens cost? (a) ₹40 (b) ₹24 (c) ₹20 (d) ₹11
4. 4.If 9 notebooks cost ₹171, how much do 3 notebooks cost? (a) ₹76 (b) ₹513 (c) ₹165 (d) ₹57
5. 5.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹104 (b) ₹65 (c) ₹117 (d) ₹13
6. 6.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹60 (d) ₹30
7. 7.If 8 pens cost ₹184, how much do 12 pens cost? (a) ₹299 (b) ₹188 (c) ₹2208 (d) ₹276
8. 8.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 7 days (d) 8 days
9. 9.If 5 kites cost ₹30, how much do 11 kites cost? (a) ₹72 (b) ₹36 (c) ₹66 (d) ₹330
10. 10.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹60 (d) ₹36
11. 11.If 3 kites cost ₹72, how much do 9 kites cost? (a) ₹78 (b) ₹648 (c) ₹216 (d) ₹240
12. 12.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
13. 13.₹200 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹200 (b) ₹100 (c) ₹25 (d) ₹175
14. 14.If 2 kites cost ₹50, how much do 8 kites cost? (a) ₹225 (b) ₹400 (c) ₹56 (d) ₹200
15. 15.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹56 (d) ₹28
16. 16.If 4 pens cost ₹92, how much do 5 pens cost? (a) ₹138 (b) ₹115 (c) ₹460 (d) ₹93
17. 17.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹288 (b) ₹234 (c) ₹180 (d) ₹36
18. 18.If 2 kites cost ₹6, how much do 4 kites cost? (a) ₹24 (b) ₹12 (c) ₹15 (d) ₹8
19. 19.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹56 (d) ₹48
20. 20.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹77 (b) ₹66 (c) ₹55 (d) ₹11
21. 21.If 5 kites cost ₹105, how much do 10 kites cost? (a) ₹110 (b) ₹231 (c) ₹1050 (d) ₹210
22. 22.If 4 pens cost ₹28, how much do 6 pens cost? (a) ₹30 (b) ₹42 (c) ₹49 (d) ₹168
23. 23.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹46 (b) ₹207 (c) ₹230 (d) ₹23
24. 24.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹414 (d) ₹322
25. 25.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹276 (b) ₹253 (c) ₹46 (d) ₹230
26. 26.If 3 mangoes cost ₹75, how much do 4 mangoes cost? (a) ₹100 (b) ₹125 (c) ₹300 (d) ₹76
27. 27.If 4 pens cost ₹64, how much do 3 pens cost? (a) ₹63 (b) ₹64 (c) ₹192 (d) ₹48
28. 28.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹195 (b) ₹234 (c) ₹39 (d) ₹273
29. 29.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 28 days (d) 7 days
30. 30.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹333 (d) ₹259
31. 31.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹72 (d) ₹42
32. 32.If 5 kites cost ₹40, how much do 7 kites cost? (a) ₹280 (b) ₹64 (c) ₹56 (d) ₹42
33. 33.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹189 (b) ₹162 (c) ₹27 (d) ₹163
34. 34.If 3 kites cost ₹48, how much do 11 kites cost? (a) ₹56 (b) ₹192 (c) ₹528 (d) ₹176
35. 35.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 45 days (c) 5 days (d) 19 days
36. 36.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 37 days (d) 36 days
37. 37.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 2 days (d) 12 days
38. 38.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹80 (c) ₹50 (d) ₹10
39. 39.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹44 (d) ₹88
40. 40.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 4 days

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