Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 286 · 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.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹300 (b) ₹30 (c) ₹270 (d) ₹150
2. 2.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹216 (b) ₹243 (c) ₹217 (d) ₹27
3. 3.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 5 days (d) 6 days
4. 4.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 14 days (c) 5 days (d) 6 days
5. 5.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 13 days
6. 6.If 5 mangoes cost ₹25, how much do 7 mangoes cost? (a) ₹40 (b) ₹175 (c) ₹35 (d) ₹27
7. 7.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹19 (d) ₹57
8. 8.If 8 pens cost ₹152, how much do 5 pens cost? (a) ₹760 (b) ₹95 (c) ₹114 (d) ₹149
9. 9.If 5 kites cost ₹105, how much do 3 kites cost? (a) ₹315 (b) ₹63 (c) ₹84 (d) ₹103
10. 10.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹96 (b) ₹24 (c) ₹132 (d) ₹168
11. 11.If 4 mangoes cost ₹32, how much do 2 mangoes cost? (a) ₹24 (b) ₹64 (c) ₹16 (d) ₹30
12. 12.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 4 days (d) 25 days
13. 13.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 6 days (d) 4 days
14. 14.If 5 mangoes cost ₹35, how much do 12 mangoes cost? (a) ₹42 (b) ₹420 (c) ₹91 (d) ₹84
15. 15.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 21 days (c) 3 days (d) 48 days
16. 16.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 9 days (d) 15 days
17. 17.If 2 mangoes cost ₹20, how much do 12 mangoes cost? (a) ₹240 (b) ₹30 (c) ₹130 (d) ₹120
18. 18.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹44 (c) ₹220 (d) ₹176
19. 19.If 3 notebooks cost ₹72, how much do 4 notebooks cost? (a) ₹288 (b) ₹120 (c) ₹73 (d) ₹96
20. 20.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 3 days (c) 21 days (d) 11 days
21. 21.4 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) 10 days (d) 13 days
22. 22.If 3 pens cost ₹12, how much do 12 pens cost? (a) ₹21 (b) ₹48 (c) ₹144 (d) ₹52
23. 23.If 3 notebooks cost ₹51, how much do 5 notebooks cost? (a) ₹53 (b) ₹85 (c) ₹255 (d) ₹102
24. 24.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 7 days (d) 12 days
25. 25.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹441 (b) ₹49 (c) ₹392 (d) ₹147
26. 26.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 19 days
27. 27.If 9 notebooks cost ₹126, how much do 8 notebooks cost? (a) ₹112 (b) ₹126 (c) ₹1008 (d) ₹125
28. 28.If 5 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹32 (b) ₹140 (c) ₹28 (d) ₹22
29. 29.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹232 (b) ₹203 (c) ₹116 (d) ₹29
30. 30.If 4 notebooks cost ₹20, how much do 5 notebooks cost? (a) ₹25 (b) ₹100 (c) ₹21 (d) ₹30
31. 31.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹55 (b) ₹10 (c) ₹70 (d) ₹40
32. 32.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 18 days (b) 15 days (c) 8 days (d) 9 days
33. 33.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹55 (b) ₹110 (c) ₹11 (d) ₹99
34. 34.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 27 days (d) 17 days
35. 35.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 9 days (d) 15 days
36. 36.9 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) 10 days (d) 5 days
37. 37.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 12 days (d) 8 days
38. 38.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 25 days (d) 13 days
39. 39.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 10 days (d) 14 days
40. 40.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 13 days

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