Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 637 · 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 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 16 days (d) 4 days
2. 2.If 2 mangoes cost ₹46, how much do 11 mangoes cost? (a) ₹276 (b) ₹55 (c) ₹506 (d) ₹253
3. 3.If 5 mangoes cost ₹70, how much do 2 mangoes cost? (a) ₹67 (b) ₹140 (c) ₹42 (d) ₹28
4. 4.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹54 (b) ₹9 (c) ₹45 (d) ₹63
5. 5.If 3 pens cost ₹21, how much do 8 pens cost? (a) ₹168 (b) ₹26 (c) ₹63 (d) ₹56
6. 6.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 24 days (c) 8 days (d) 6 days
7. 7.If 8 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹240 (b) ₹33 (c) ₹26 (d) ₹30
8. 8.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹252 (d) ₹216
9. 9.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹125 (b) ₹50 (c) ₹150 (d) ₹25
10. 10.If 9 pens cost ₹27, how much do 10 pens cost? (a) ₹28 (b) ₹30 (c) ₹270 (d) ₹33
11. 11.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 18 days
12. 12.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 17 days (d) 10 days
13. 13.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
14. 14.₹162 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹36 (b) ₹126 (c) ₹18 (d) ₹81
15. 15.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 25 days (c) 24 days (d) 12 days
16. 16.If 4 kites cost ₹80, how much do 10 kites cost? (a) ₹86 (b) ₹200 (c) ₹800 (d) ₹220
17. 17.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 21 days (c) 5 days (d) 11 days
18. 18.₹140 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹70 (d) ₹112
19. 19.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 12 days (c) 16 days (d) 4 days
20. 20.If 8 kites cost ₹200, how much do 10 kites cost? (a) ₹2000 (b) ₹250 (c) ₹275 (d) ₹202
21. 21.If 7 mangoes cost ₹35, how much do 3 mangoes cost? (a) ₹31 (b) ₹105 (c) ₹20 (d) ₹15
22. 22.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 15 days (d) 3 days
23. 23.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹235 (b) ₹273 (c) ₹234 (d) ₹39
24. 24.If 3 pens cost ₹39, how much do 10 pens cost? (a) ₹130 (b) ₹390 (c) ₹143 (d) ₹46
25. 25.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹195 (b) ₹117 (c) ₹234 (d) ₹39
26. 26.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹35 (c) ₹7 (d) ₹42
27. 27.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹336 (b) ₹189 (c) ₹378 (d) ₹42
28. 28.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 2 days (c) 16 days (d) 1 day
29. 29.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 17 days (c) 11 days (d) 36 days
30. 30.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹35 (c) ₹175 (d) ₹140
31. 31.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 31 days (c) 16 days (d) 30 days
32. 32.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹123 (b) ₹205 (c) ₹164 (d) ₹41
33. 33.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹38 (b) ₹114 (c) ₹57 (d) ₹76
34. 34.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 15 days (c) 1 day (d) 36 days
35. 35.If 8 pens cost ₹24, how much do 9 pens cost? (a) ₹25 (b) ₹30 (c) ₹216 (d) ₹27
36. 36.If 3 pens cost ₹42, how much do 5 pens cost? (a) ₹44 (b) ₹210 (c) ₹84 (d) ₹70
37. 37.If 6 mangoes cost ₹108, how much do 8 mangoes cost? (a) ₹110 (b) ₹864 (c) ₹144 (d) ₹162
38. 38.If 8 pens cost ₹136, how much do 4 pens cost? (a) ₹85 (b) ₹68 (c) ₹132 (d) ₹544
39. 39.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹245 (b) ₹294 (c) ₹343 (d) ₹49
40. 40.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 36 days (d) 35 days

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