Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 802 · 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. 1.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 2 days (d) 4 days
2. 2.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹40 (d) ₹80
3. 3.If 5 pens cost ₹95, how much do 4 pens cost? (a) ₹94 (b) ₹95 (c) ₹76 (d) ₹380
4. 4.If 8 mangoes cost ₹88, how much do 2 mangoes cost? (a) ₹176 (b) ₹82 (c) ₹33 (d) ₹22
5. 5.₹77 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹66 (d) ₹22
6. 6.If 7 kites cost ₹168, how much do 8 kites cost? (a) ₹169 (b) ₹1344 (c) ₹192 (d) ₹216
7. 7.If 7 pens cost ₹112, how much do 8 pens cost? (a) ₹113 (b) ₹144 (c) ₹128 (d) ₹896
8. 8.If 8 mangoes cost ₹88, how much do 6 mangoes cost? (a) ₹528 (b) ₹66 (c) ₹86 (d) ₹77
9. 9.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 3 days (d) 2 days
10. 10.If 6 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹104 (b) ₹576 (c) ₹54 (d) ₹96
11. 11.If 4 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹35 (b) ₹29 (c) ₹140 (d) ₹42
12. 12.If 9 kites cost ₹99, how much do 2 kites cost? (a) ₹22 (b) ₹198 (c) ₹92 (d) ₹33
13. 13.If 9 kites cost ₹225, how much do 10 kites cost? (a) ₹226 (b) ₹2250 (c) ₹250 (d) ₹275
14. 14.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹95 (b) ₹19 (c) ₹76 (d) ₹77
15. 15.If 8 pens cost ₹56, how much do 4 pens cost? (a) ₹224 (b) ₹52 (c) ₹35 (d) ₹28
16. 16.If 8 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹48 (b) ₹36 (c) ₹52 (d) ₹384
17. 17.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹55 (b) ₹22 (c) ₹66 (d) ₹44
18. 18.₹216 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹216 (b) ₹108 (c) ₹180 (d) ₹36
19. 19.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
20. 20.If 5 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹51 (b) ₹300 (c) ₹60 (d) ₹70
21. 21.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 10 days (d) 28 days
22. 22.If 2 pens cost ₹8, how much do 6 pens cost? (a) ₹48 (b) ₹28 (c) ₹12 (d) ₹24
23. 23.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 13 days (d) 10 days
24. 24.If 2 notebooks cost ₹20, how much do 11 notebooks cost? (a) ₹29 (b) ₹220 (c) ₹120 (d) ₹110
25. 25.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹259 (d) ₹296
26. 26.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 3 days (d) 29 days
27. 27.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹30 (c) ₹20 (d) ₹5
28. 28.If 2 pens cost ₹6, how much do 9 pens cost? (a) ₹27 (b) ₹30 (c) ₹54 (d) ₹13
29. 29.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹71 (b) ₹176 (c) ₹528 (d) ₹198
30. 30.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹7 (d) ₹57
31. 31.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹48 (b) ₹84 (c) ₹12 (d) ₹66
32. 32.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 10 days (d) 1 day
33. 33.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 13 days
34. 34.If 5 kites cost ₹70, how much do 2 kites cost? (a) ₹42 (b) ₹67 (c) ₹140 (d) ₹28
35. 35.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 7 days (d) 28 days
36. 36.₹168 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹168 (b) ₹144 (c) ₹84 (d) ₹24
37. 37.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 20 days (c) 5 days (d) 21 days
38. 38.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 9 days (d) 4 days
39. 39.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 4 days (d) 9 days
40. 40.If 7 notebooks cost ₹154, how much do 11 notebooks cost? (a) ₹1694 (b) ₹264 (c) ₹158 (d) ₹242

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