Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 399 · 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 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 12 days (d) 8 days
2. 2.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 22 days (d) 23 days
3. 3.If 8 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹15 (b) ₹10 (c) ₹34 (d) ₹80
4. 4.If 5 notebooks cost ₹55, how much do 2 notebooks cost? (a) ₹52 (b) ₹33 (c) ₹110 (d) ₹22
5. 5.If 2 notebooks cost ₹40, how much do 7 notebooks cost? (a) ₹160 (b) ₹140 (c) ₹45 (d) ₹280
6. 6.4 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) 2 days (d) 11 days
7. 7.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 7 days
8. 8.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹24 (d) ₹48
9. 9.If 9 pens cost ₹216, how much do 2 pens cost? (a) ₹72 (b) ₹432 (c) ₹209 (d) ₹48
10. 10.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹225 (d) ₹315
11. 11.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 7 days (d) 3 days
12. 12.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹86 (b) ₹129 (c) ₹43 (d) ₹87
13. 13.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 1 day (d) 16 days
14. 14.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹30 (b) ₹35 (c) ₹10 (d) ₹40
15. 15.If 4 notebooks cost ₹88, how much do 5 notebooks cost? (a) ₹440 (b) ₹132 (c) ₹110 (d) ₹89
16. 16.If 5 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹18 (b) ₹90 (c) ₹24 (d) ₹28
17. 17.If 9 kites cost ₹63, how much do 6 kites cost? (a) ₹378 (b) ₹60 (c) ₹42 (d) ₹49
18. 18.If 9 kites cost ₹81, how much do 4 kites cost? (a) ₹45 (b) ₹324 (c) ₹76 (d) ₹36
19. 19.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 10 days (d) 12 days
20. 20.If 2 mangoes cost ₹36, how much do 5 mangoes cost? (a) ₹180 (b) ₹39 (c) ₹90 (d) ₹108
21. 21.If 2 mangoes cost ₹34, how much do 11 mangoes cost? (a) ₹204 (b) ₹187 (c) ₹43 (d) ₹374
22. 22.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 14 days (d) 24 days
23. 23.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 3 days (d) 27 days
24. 24.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 13 days (c) 19 days (d) 3 days
25. 25.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹12 (b) ₹96 (c) ₹108 (d) ₹54
26. 26.If 5 pens cost ₹105, how much do 3 pens cost? (a) ₹103 (b) ₹84 (c) ₹315 (d) ₹63
27. 27.If 7 notebooks cost ₹105, how much do 8 notebooks cost? (a) ₹106 (b) ₹135 (c) ₹840 (d) ₹120
28. 28.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹36 (c) ₹12 (d) ₹84
29. 29.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 10 days (d) 19 days
30. 30.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 28 days (d) 15 days
31. 31.If 7 kites cost ₹77, how much do 5 kites cost? (a) ₹66 (b) ₹55 (c) ₹385 (d) ₹75
32. 32.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 11 days (d) 4 days
33. 33.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 11 days
34. 34.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 13 days (d) 3 days
35. 35.If 5 kites cost ₹15, how much do 4 kites cost? (a) ₹14 (b) ₹15 (c) ₹12 (d) ₹60
36. 36.If 4 kites cost ₹72, how much do 11 kites cost? (a) ₹198 (b) ₹216 (c) ₹79 (d) ₹792
37. 37.If 8 pens cost ₹88, how much do 9 pens cost? (a) ₹89 (b) ₹110 (c) ₹99 (d) ₹792
38. 38.If 8 pens cost ₹80, how much do 4 pens cost? (a) ₹40 (b) ₹50 (c) ₹76 (d) ₹320
39. 39.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 12 days (d) 24 days
40. 40.If 7 pens cost ₹91, how much do 10 pens cost? (a) ₹130 (b) ₹910 (c) ₹94 (d) ₹143

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