Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 449 · 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. 1.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 26 days (c) 28 days (d) 27 days
2. 2.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 5 days
3. 3.If 7 mangoes cost ₹105, how much do 9 mangoes cost? (a) ₹107 (b) ₹150 (c) ₹945 (d) ₹135
4. 4.If 5 mangoes cost ₹95, how much do 3 mangoes cost? (a) ₹76 (b) ₹93 (c) ₹57 (d) ₹285
5. 5.If 9 kites cost ₹36, how much do 4 kites cost? (a) ₹31 (b) ₹144 (c) ₹20 (d) ₹16
6. 6.If 2 mangoes cost ₹10, how much do 9 mangoes cost? (a) ₹50 (b) ₹17 (c) ₹45 (d) ₹90
7. 7.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 17 days (d) 11 days
8. 8.If 4 notebooks cost ₹16, how much do 5 notebooks cost? (a) ₹20 (b) ₹80 (c) ₹24 (d) ₹17
9. 9.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 4 days (d) 3 days
10. 10.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 13 days (d) 9 days
11. 11.If 7 notebooks cost ₹147, how much do 3 notebooks cost? (a) ₹63 (b) ₹441 (c) ₹143 (d) ₹84
12. 12.₹155 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹155 (b) ₹124 (c) ₹125 (d) ₹31
13. 13.If 2 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹22 (b) ₹40 (c) ₹80 (d) ₹50
14. 14.₹140 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹84 (d) ₹70
15. 15.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 9 days (d) 15 days
16. 16.₹234 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹117 (b) ₹182 (c) ₹26 (d) ₹52
17. 17.If 7 kites cost ₹126, how much do 4 kites cost? (a) ₹123 (b) ₹90 (c) ₹72 (d) ₹504
18. 18.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹143 (b) ₹182 (c) ₹26 (d) ₹104
19. 19.If 8 pens cost ₹88, how much do 2 pens cost? (a) ₹33 (b) ₹176 (c) ₹82 (d) ₹22
20. 20.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 16 days (d) 13 days
21. 21.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹38 (b) ₹190 (c) ₹19 (d) ₹171
22. 22.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 7 days (d) 5 days
23. 23.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹215 (b) ₹387 (c) ₹301 (d) ₹43
24. 24.If 2 pens cost ₹50, how much do 10 pens cost? (a) ₹58 (b) ₹500 (c) ₹275 (d) ₹250
25. 25.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 15 days (d) 1 day
26. 26.If 7 pens cost ₹35, how much do 9 pens cost? (a) ₹37 (b) ₹315 (c) ₹45 (d) ₹50
27. 27.₹114 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹95 (b) ₹19 (c) ₹114 (d) ₹57
28. 28.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹138 (b) ₹92 (c) ₹115 (d) ₹23
29. 29.If 5 pens cost ₹120, how much do 12 pens cost? (a) ₹127 (b) ₹1440 (c) ₹288 (d) ₹312
30. 30.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 11 days (d) 19 days
31. 31.If 3 kites cost ₹48, how much do 7 kites cost? (a) ₹128 (b) ₹336 (c) ₹112 (d) ₹52
32. 32.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 8 days (d) 16 days
33. 33.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 24 days (c) 14 days (d) 25 days
34. 34.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 6 days (d) 19 days
35. 35.If 4 pens cost ₹16, how much do 5 pens cost? (a) ₹20 (b) ₹80 (c) ₹24 (d) ₹17
36. 36.If 4 kites cost ₹60, how much do 7 kites cost? (a) ₹63 (b) ₹120 (c) ₹105 (d) ₹420
37. 37.If 7 mangoes cost ₹126, how much do 11 mangoes cost? (a) ₹130 (b) ₹216 (c) ₹198 (d) ₹1386
38. 38.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹105 (b) ₹75 (c) ₹135 (d) ₹15
39. 39.If 3 pens cost ₹75, how much do 7 pens cost? (a) ₹79 (b) ₹200 (c) ₹525 (d) ₹175
40. 40.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 2 days

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