Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 376 · 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. 1.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 16 days (d) 4 days
2. 2.If 3 kites cost ₹39, how much do 4 kites cost? (a) ₹156 (b) ₹40 (c) ₹65 (d) ₹52
3. 3.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹117 (b) ₹13 (c) ₹130 (d) ₹65
4. 4.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹120 (d) ₹135
5. 5.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 26 days (d) 28 days
6. 6.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹258 (b) ₹86 (c) ₹43 (d) ₹215
7. 7.₹369 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹41 (b) ₹328 (c) ₹369 (d) ₹329
8. 8.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 10 days (d) 9 days
9. 9.If 9 notebooks cost ₹63, how much do 10 notebooks cost? (a) ₹77 (b) ₹64 (c) ₹70 (d) ₹630
10. 10.If 7 kites cost ₹154, how much do 3 kites cost? (a) ₹462 (b) ₹66 (c) ₹150 (d) ₹88
11. 11.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
12. 12.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 14 days (d) 16 days
13. 13.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹14 (c) ₹112 (d) ₹126
14. 14.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 2 days
15. 15.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹148 (b) ₹111 (c) ₹37 (d) ₹74
16. 16.If 4 pens cost ₹92, how much do 6 pens cost? (a) ₹161 (b) ₹552 (c) ₹94 (d) ₹138
17. 17.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹52 (b) ₹72 (c) ₹32 (d) ₹8
18. 18.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 10 days (d) 6 days
19. 19.If 2 pens cost ₹22, how much do 3 pens cost? (a) ₹33 (b) ₹23 (c) ₹66 (d) ₹44
20. 20.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹48 (b) ₹40 (c) ₹44 (d) ₹8
21. 21.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 27 days (d) 26 days
22. 22.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 14 days (d) 4 days
23. 23.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹72 (c) ₹84 (d) ₹12
24. 24.If 7 kites cost ₹147, how much do 10 kites cost? (a) ₹210 (b) ₹1470 (c) ₹231 (d) ₹150
25. 25.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 4 days (d) 27 days
26. 26.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 16 days (d) 4 days
27. 27.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 33 days (c) 2 days (d) 32 days
28. 28.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹12 (b) ₹36 (c) ₹60 (d) ₹84
29. 29.If 4 notebooks cost ₹32, how much do 5 notebooks cost? (a) ₹48 (b) ₹160 (c) ₹33 (d) ₹40
30. 30.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹172 (b) ₹86 (c) ₹129 (d) ₹43
31. 31.If 9 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹16 (b) ₹144 (c) ₹65 (d) ₹24
32. 32.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
33. 33.If 4 notebooks cost ₹84, how much do 2 notebooks cost? (a) ₹63 (b) ₹42 (c) ₹82 (d) ₹168
34. 34.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹44 (b) ₹440 (c) ₹220 (d) ₹396
35. 35.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹52 (c) ₹8 (d) ₹64
36. 36.If 4 kites cost ₹60, how much do 11 kites cost? (a) ₹180 (b) ₹67 (c) ₹165 (d) ₹660
37. 37.If 7 mangoes cost ₹112, how much do 3 mangoes cost? (a) ₹336 (b) ₹108 (c) ₹64 (d) ₹48
38. 38.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹180 (b) ₹90 (c) ₹30 (d) ₹150
39. 39.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹42 (b) ₹12 (c) ₹84 (d) ₹72
40. 40.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹85 (d) ₹68

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