Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 519 · 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 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 15 days (c) 16 days (d) 9 days
2. 2.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
3. 3.If 6 mangoes cost ₹90, how much do 8 mangoes cost? (a) ₹92 (b) ₹135 (c) ₹720 (d) ₹120
4. 4.If 2 notebooks cost ₹38, how much do 3 notebooks cost? (a) ₹114 (b) ₹76 (c) ₹39 (d) ₹57
5. 5.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 4 days (d) 8 days
6. 6.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹80 (c) ₹72 (d) ₹16
7. 7.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 9 days (d) 17 days
8. 8.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 14 days (c) 16 days (d) 21 days
9. 9.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 16 days (c) 19 days (d) 14 days
10. 10.If 6 kites cost ₹96, how much do 10 kites cost? (a) ₹176 (b) ₹960 (c) ₹160 (d) ₹100
11. 11.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹36 (b) ₹126 (c) ₹72 (d) ₹180
12. 12.₹266 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹190 (b) ₹76 (c) ₹133 (d) ₹38
13. 13.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 13 days (d) 14 days
14. 14.If 2 notebooks cost ₹6, how much do 10 notebooks cost? (a) ₹30 (b) ₹14 (c) ₹60 (d) ₹33
15. 15.If 6 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹252 (b) ₹37 (c) ₹48 (d) ₹42
16. 16.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹216 (b) ₹24 (c) ₹96 (d) ₹156
17. 17.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 19 days (d) 36 days
18. 18.If 8 pens cost ₹80, how much do 9 pens cost? (a) ₹720 (b) ₹100 (c) ₹90 (d) ₹81
19. 19.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 2 days
20. 20.If 8 pens cost ₹168, how much do 12 pens cost? (a) ₹2016 (b) ₹273 (c) ₹172 (d) ₹252
21. 21.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 33 days (d) 32 days
22. 22.If 7 notebooks cost ₹161, how much do 4 notebooks cost? (a) ₹158 (b) ₹644 (c) ₹115 (d) ₹92
23. 23.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹45 (b) ₹27 (c) ₹9 (d) ₹36
24. 24.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
25. 25.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 16 days (d) 12 days
26. 26.If 2 kites cost ₹40, how much do 10 kites cost? (a) ₹200 (b) ₹220 (c) ₹48 (d) ₹400
27. 27.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹270 (b) ₹120 (c) ₹195 (d) ₹30
28. 28.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 16 days (c) 5 days (d) 4 days
29. 29.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹209 (b) ₹38 (c) ₹266 (d) ₹152
30. 30.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹165 (b) ₹30 (c) ₹120 (d) ₹210
31. 31.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹216 (b) ₹180 (c) ₹252 (d) ₹36
32. 32.If 9 kites cost ₹45, how much do 6 kites cost? (a) ₹30 (b) ₹42 (c) ₹35 (d) ₹270
33. 33.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹325 (b) ₹200 (c) ₹450 (d) ₹50
34. 34.If 2 kites cost ₹8, how much do 4 kites cost? (a) ₹16 (b) ₹10 (c) ₹20 (d) ₹32
35. 35.If 9 pens cost ₹171, how much do 10 pens cost? (a) ₹1710 (b) ₹172 (c) ₹209 (d) ₹190
36. 36.If 6 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹144 (b) ₹24 (c) ₹34 (d) ₹30
37. 37.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 2 days (d) 10 days
38. 38.If 3 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹168 (b) ₹64 (c) ₹56 (d) ₹28
39. 39.If 7 kites cost ₹154, how much do 3 kites cost? (a) ₹150 (b) ₹66 (c) ₹88 (d) ₹462
40. 40.If 7 kites cost ₹70, how much do 9 kites cost? (a) ₹90 (b) ₹100 (c) ₹630 (d) ₹72

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