Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 790 · 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.If 2 mangoes cost ₹8, how much do 12 mangoes cost? (a) ₹52 (b) ₹96 (c) ₹48 (d) ₹18
2. 2.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
3. 3.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 4 days (d) 3 days
4. 4.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 42 days (c) 43 days (d) 20 days
5. 5.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 7 days (d) 11 days
6. 6.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 2 days (d) 4 days
7. 7.If 9 pens cost ₹54, how much do 10 pens cost? (a) ₹60 (b) ₹55 (c) ₹66 (d) ₹540
8. 8.9 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
9. 9.If 3 pens cost ₹69, how much do 12 pens cost? (a) ₹78 (b) ₹276 (c) ₹828 (d) ₹299
10. 10.If 3 notebooks cost ₹51, how much do 8 notebooks cost? (a) ₹136 (b) ₹56 (c) ₹408 (d) ₹153
11. 11.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 1 day (d) 4 days
12. 12.If 4 pens cost ₹16, how much do 3 pens cost? (a) ₹16 (b) ₹12 (c) ₹48 (d) ₹15
13. 13.If 4 kites cost ₹88, how much do 5 kites cost? (a) ₹110 (b) ₹89 (c) ₹440 (d) ₹132
14. 14.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 5 days (c) 7 days (d) 45 days
15. 15.If 4 notebooks cost ₹72, how much do 3 notebooks cost? (a) ₹71 (b) ₹54 (c) ₹72 (d) ₹216
16. 16.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 3 days (d) 13 days
17. 17.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹231 (b) ₹42 (c) ₹336 (d) ₹126
18. 18.If 3 notebooks cost ₹48, how much do 6 notebooks cost? (a) ₹112 (b) ₹96 (c) ₹51 (d) ₹288
19. 19.If 8 kites cost ₹24, how much do 5 kites cost? (a) ₹18 (b) ₹15 (c) ₹21 (d) ₹120
20. 20.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 11 days (d) 26 days
21. 21.If 6 mangoes cost ₹30, how much do 2 mangoes cost? (a) ₹26 (b) ₹15 (c) ₹10 (d) ₹60
22. 22.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹176 (d) ₹198
23. 23.6 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) 24 days (d) 12 days
24. 24.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 15 days (d) 12 days
25. 25.If 9 mangoes cost ₹153, how much do 2 mangoes cost? (a) ₹51 (b) ₹146 (c) ₹34 (d) ₹306
26. 26.₹200 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹175 (b) ₹200 (c) ₹100 (d) ₹25
27. 27.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 2 days (d) 18 days
28. 28.If 6 mangoes cost ₹138, how much do 10 mangoes cost? (a) ₹142 (b) ₹1380 (c) ₹253 (d) ₹230
29. 29.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 6 days
30. 30.If 3 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹15 (b) ₹24 (c) ₹72 (d) ₹28
31. 31.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹10 (b) ₹5 (c) ₹35 (d) ₹40
32. 32.If 2 pens cost ₹38, how much do 6 pens cost? (a) ₹42 (b) ₹133 (c) ₹114 (d) ₹228
33. 33.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 16 days (c) 21 days (d) 12 days
34. 34.If 9 pens cost ₹171, how much do 4 pens cost? (a) ₹684 (b) ₹76 (c) ₹166 (d) ₹95
35. 35.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹48 (b) ₹64 (c) ₹56 (d) ₹16
36. 36.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹56 (d) ₹35
37. 37.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹161 (b) ₹69 (c) ₹23 (d) ₹115
38. 38.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹77 (b) ₹22 (c) ₹66 (d) ₹88
39. 39.If 4 mangoes cost ₹92, how much do 10 mangoes cost? (a) ₹230 (b) ₹253 (c) ₹920 (d) ₹98
40. 40.₹320 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹320 (b) ₹160 (c) ₹40 (d) ₹280

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