Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 565 · 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. 1.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 23 days (d) 14 days
2. 2.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹405 (b) ₹225 (c) ₹45 (d) ₹360
3. 3.If 9 pens cost ₹216, how much do 8 pens cost? (a) ₹1728 (b) ₹215 (c) ₹192 (d) ₹216
4. 4.If 4 kites cost ₹80, how much do 7 kites cost? (a) ₹83 (b) ₹160 (c) ₹560 (d) ₹140
5. 5.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 15 days (d) 3 days
6. 6.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹48 (b) ₹192 (c) ₹240 (d) ₹144
7. 7.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 7 days (d) 8 days
8. 8.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
9. 9.If 8 pens cost ₹24, how much do 4 pens cost? (a) ₹15 (b) ₹96 (c) ₹12 (d) ₹20
10. 10.If 6 pens cost ₹84, how much do 9 pens cost? (a) ₹126 (b) ₹756 (c) ₹140 (d) ₹87
11. 11.If 4 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹27 (b) ₹34 (c) ₹18 (d) ₹72
12. 12.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹138 (c) ₹46 (d) ₹92
13. 13.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 8 days (d) 9 days
14. 14.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 16 days (d) 4 days
15. 15.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 21 days (c) 13 days (d) 22 days
16. 16.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 44 days (c) 5 days (d) 45 days
17. 17.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 17 days (d) 4 days
18. 18.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹24 (d) ₹28
19. 19.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 7 days (d) 4 days
20. 20.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 11 days (d) 36 days
21. 21.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹78 (b) ₹91 (c) ₹13 (d) ₹65
22. 22.If 4 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹35 (b) ₹42 (c) ₹29 (d) ₹140
23. 23.If 3 kites cost ₹21, how much do 6 kites cost? (a) ₹49 (b) ₹126 (c) ₹42 (d) ₹24
24. 24.₹224 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹112 (d) ₹84
25. 25.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 6 days (d) 20 days
26. 26.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹91 (b) ₹14 (c) ₹70 (d) ₹112
27. 27.If 4 notebooks cost ₹88, how much do 2 notebooks cost? (a) ₹44 (b) ₹66 (c) ₹176 (d) ₹86
28. 28.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 13 days (d) 11 days
29. 29.If 5 pens cost ₹105, how much do 3 pens cost? (a) ₹84 (b) ₹63 (c) ₹315 (d) ₹103
30. 30.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 7 days
31. 31.8 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
32. 32.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 13 days (d) 5 days
33. 33.If 4 notebooks cost ₹76, how much do 5 notebooks cost? (a) ₹114 (b) ₹77 (c) ₹380 (d) ₹95
34. 34.If 5 notebooks cost ₹95, how much do 11 notebooks cost? (a) ₹101 (b) ₹209 (c) ₹228 (d) ₹1045
35. 35.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹312 (b) ₹48 (c) ₹240 (d) ₹384
36. 36.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹121 (b) ₹132 (c) ₹22 (d) ₹110
37. 37.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
38. 38.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹112 (b) ₹144 (c) ₹80 (d) ₹16
39. 39.If 7 kites cost ₹91, how much do 8 kites cost? (a) ₹104 (b) ₹117 (c) ₹92 (d) ₹728
40. 40.If 3 notebooks cost ₹15, how much do 10 notebooks cost? (a) ₹50 (b) ₹150 (c) ₹22 (d) ₹55

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