Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 13 · 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. 1.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 7 days (d) 11 days
2. 2.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹128 (c) ₹160 (d) ₹32
3. 3.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 2 days (d) 8 days
4. 4.If 6 notebooks cost ₹18, how much do 2 notebooks cost? (a) ₹36 (b) ₹6 (c) ₹9 (d) ₹14
5. 5.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 18 days (d) 36 days
6. 6.If 7 notebooks cost ₹28, how much do 2 notebooks cost? (a) ₹8 (b) ₹23 (c) ₹12 (d) ₹56
7. 7.5 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) 4 days (d) 17 days
8. 8.If 5 notebooks cost ₹110, how much do 6 notebooks cost? (a) ₹154 (b) ₹132 (c) ₹660 (d) ₹111
9. 9.₹152 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹114 (c) ₹38 (d) ₹152
10. 10.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹147 (d) ₹126
11. 11.If 5 mangoes cost ₹95, how much do 7 mangoes cost? (a) ₹133 (b) ₹97 (c) ₹665 (d) ₹152
12. 12.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹152 (b) ₹38 (c) ₹133 (d) ₹114
13. 13.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹253 (b) ₹46 (c) ₹230 (d) ₹276
14. 14.If 4 kites cost ₹72, how much do 2 kites cost? (a) ₹70 (b) ₹144 (c) ₹36 (d) ₹54
15. 15.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹7 (c) ₹28 (d) ₹49
16. 16.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 6 days (c) 18 days (d) 4 days
17. 17.If 6 mangoes cost ₹30, how much do 2 mangoes cost? (a) ₹15 (b) ₹60 (c) ₹26 (d) ₹10
18. 18.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 20 days (d) 4 days
19. 19.If 5 notebooks cost ₹85, how much do 11 notebooks cost? (a) ₹935 (b) ₹204 (c) ₹91 (d) ₹187
20. 20.If 7 pens cost ₹161, how much do 8 pens cost? (a) ₹1288 (b) ₹207 (c) ₹184 (d) ₹162
21. 21.If 2 pens cost ₹14, how much do 4 pens cost? (a) ₹35 (b) ₹16 (c) ₹56 (d) ₹28
22. 22.If 5 kites cost ₹95, how much do 6 kites cost? (a) ₹114 (b) ₹96 (c) ₹133 (d) ₹570
23. 23.If 9 kites cost ₹189, how much do 2 kites cost? (a) ₹42 (b) ₹182 (c) ₹63 (d) ₹378
24. 24.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹79 (b) ₹78 (c) ₹91 (d) ₹13
25. 25.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 20 days (d) 13 days
26. 26.If 5 mangoes cost ₹25, how much do 10 mangoes cost? (a) ₹30 (b) ₹250 (c) ₹55 (d) ₹50
27. 27.If 8 kites cost ₹120, how much do 11 kites cost? (a) ₹180 (b) ₹123 (c) ₹165 (d) ₹1320
28. 28.If 8 pens cost ₹56, how much do 7 pens cost? (a) ₹56 (b) ₹49 (c) ₹55 (d) ₹392
29. 29.7 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) 5 days (d) 21 days
30. 30.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 9 days
31. 31.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹72 (d) ₹45
32. 32.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹126 (b) ₹28 (c) ₹56 (d) ₹196
33. 33.If 3 kites cost ₹15, how much do 4 kites cost? (a) ₹25 (b) ₹20 (c) ₹16 (d) ₹60
34. 34.If 3 notebooks cost ₹75, how much do 11 notebooks cost? (a) ₹300 (b) ₹83 (c) ₹825 (d) ₹275
35. 35.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 19 days (d) 12 days
36. 36.If 6 kites cost ₹18, how much do 12 kites cost? (a) ₹24 (b) ₹39 (c) ₹216 (d) ₹36
37. 37.If 4 kites cost ₹28, how much do 7 kites cost? (a) ₹31 (b) ₹56 (c) ₹196 (d) ₹49
38. 38.If 2 notebooks cost ₹12, how much do 3 notebooks cost? (a) ₹24 (b) ₹18 (c) ₹13 (d) ₹36
39. 39.If 3 pens cost ₹60, how much do 9 pens cost? (a) ₹200 (b) ₹540 (c) ₹66 (d) ₹180
40. 40.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 7 days (d) 21 days

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