Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 708 · 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 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 7 days (d) 8 days
2. 2.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹20 (c) ₹5 (d) ₹10
3. 3.If 4 pens cost ₹28, how much do 2 pens cost? (a) ₹14 (b) ₹21 (c) ₹56 (d) ₹26
4. 4.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 8 days
5. 5.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹45 (c) ₹81 (d) ₹9
6. 6.₹484 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹88 (b) ₹396 (c) ₹242 (d) ₹44
7. 7.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 16 days (d) 10 days
8. 8.If 2 mangoes cost ₹44, how much do 12 mangoes cost? (a) ₹528 (b) ₹54 (c) ₹264 (d) ₹286
9. 9.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹61 (b) ₹100 (c) ₹80 (d) ₹240
10. 10.If 6 pens cost ₹36, how much do 10 pens cost? (a) ₹360 (b) ₹66 (c) ₹40 (d) ₹60
11. 11.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 9 days (d) 14 days
12. 12.If 3 notebooks cost ₹66, how much do 6 notebooks cost? (a) ₹396 (b) ₹69 (c) ₹154 (d) ₹132
13. 13.If 6 kites cost ₹60, how much do 2 kites cost? (a) ₹120 (b) ₹30 (c) ₹56 (d) ₹20
14. 14.If 4 kites cost ₹20, how much do 8 kites cost? (a) ₹45 (b) ₹24 (c) ₹40 (d) ₹160
15. 15.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹65 (b) ₹39 (c) ₹52 (d) ₹13
16. 16.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹6 (b) ₹18 (c) ₹24 (d) ₹30
17. 17.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹140 (b) ₹80 (c) ₹20 (d) ₹110
18. 18.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 17 days
19. 19.₹460 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹414 (d) ₹460
20. 20.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 17 days (d) 19 days
21. 21.If 4 mangoes cost ₹84, how much do 6 mangoes cost? (a) ₹147 (b) ₹504 (c) ₹86 (d) ₹126
22. 22.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹28 (c) ₹140 (d) ₹112
23. 23.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹7 (d) ₹35
24. 24.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 11 days (d) 13 days
25. 25.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹45 (b) ₹30 (c) ₹60 (d) ₹15
26. 26.If 8 pens cost ₹184, how much do 2 pens cost? (a) ₹69 (b) ₹368 (c) ₹178 (d) ₹46
27. 27.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 9 days (d) 23 days
28. 28.If 3 mangoes cost ₹33, how much do 8 mangoes cost? (a) ₹99 (b) ₹264 (c) ₹88 (d) ₹38
29. 29.If 7 pens cost ₹154, how much do 6 pens cost? (a) ₹924 (b) ₹154 (c) ₹153 (d) ₹132
30. 30.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹36 (b) ₹24 (c) ₹13 (d) ₹18
31. 31.If 3 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹55 (b) ₹90 (c) ₹216 (d) ₹72
32. 32.If 2 pens cost ₹44, how much do 5 pens cost? (a) ₹220 (b) ₹110 (c) ₹47 (d) ₹132
33. 33.If 8 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹224 (b) ₹32 (c) ₹28 (d) ₹31
34. 34.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹38 (b) ₹133 (c) ₹152 (d) ₹19
35. 35.If 5 pens cost ₹50, how much do 8 pens cost? (a) ₹90 (b) ₹80 (c) ₹400 (d) ₹53
36. 36.If 3 pens cost ₹18, how much do 9 pens cost? (a) ₹162 (b) ₹24 (c) ₹60 (d) ₹54
37. 37.If 8 pens cost ₹64, how much do 6 pens cost? (a) ₹62 (b) ₹56 (c) ₹384 (d) ₹48
38. 38.9 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) 24 days (d) 2 days
39. 39.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 3 days
40. 40.If 4 kites cost ₹60, how much do 11 kites cost? (a) ₹660 (b) ₹180 (c) ₹165 (d) ₹67

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