Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 338 · 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 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 28 days (d) 7 days
2. 2.If 4 mangoes cost ₹56, how much do 12 mangoes cost? (a) ₹182 (b) ₹672 (c) ₹64 (d) ₹168
3. 3.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
4. 4.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
5. 5.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹185 (b) ₹37 (c) ₹333 (d) ₹296
6. 6.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 1 day (d) 17 days
7. 7.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹117 (d) ₹234
8. 8.If 7 mangoes cost ₹175, how much do 10 mangoes cost? (a) ₹1750 (b) ₹275 (c) ₹250 (d) ₹178
9. 9.If 4 kites cost ₹56, how much do 11 kites cost? (a) ₹154 (b) ₹168 (c) ₹63 (d) ₹616
10. 10.If 3 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹100 (b) ₹270 (c) ₹90 (d) ₹36
11. 11.If 7 notebooks cost ₹28, how much do 12 notebooks cost? (a) ₹336 (b) ₹48 (c) ₹33 (d) ₹52
12. 12.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹155 (b) ₹217 (c) ₹93 (d) ₹31
13. 13.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹105 (b) ₹70 (c) ₹35 (d) ₹71
14. 14.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹83 (b) ₹82 (c) ₹41 (d) ₹123
15. 15.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 20 days (d) 11 days
16. 16.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 21 days (c) 14 days (d) 20 days
17. 17.If 2 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹60 (b) ₹120 (c) ₹41 (d) ₹80
18. 18.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹44 (c) ₹352 (d) ₹242
19. 19.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹25 (c) ₹40 (d) ₹5
20. 20.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 56 days (c) 8 days (d) 20 days
21. 21.If 6 notebooks cost ₹66, how much do 2 notebooks cost? (a) ₹132 (b) ₹33 (c) ₹22 (d) ₹62
22. 22.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 14 days (c) 15 days (d) 10 days
23. 23.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹242 (d) ₹308
24. 24.₹168 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹84 (d) ₹168
25. 25.If 8 kites cost ₹200, how much do 11 kites cost? (a) ₹2200 (b) ₹275 (c) ₹203 (d) ₹300
26. 26.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹58 (d) ₹87
27. 27.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹36 (d) ₹32
28. 28.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 21 days (d) 17 days
29. 29.If 8 mangoes cost ₹152, how much do 10 mangoes cost? (a) ₹209 (b) ₹1520 (c) ₹190 (d) ₹154
30. 30.₹506 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹253 (d) ₹368
31. 31.If 4 mangoes cost ₹44, how much do 10 mangoes cost? (a) ₹121 (b) ₹440 (c) ₹110 (d) ₹50
32. 32.If 8 pens cost ₹200, how much do 10 pens cost? (a) ₹202 (b) ₹2000 (c) ₹275 (d) ₹250
33. 33.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹78 (d) ₹91
34. 34.If 2 notebooks cost ₹8, how much do 10 notebooks cost? (a) ₹80 (b) ₹44 (c) ₹16 (d) ₹40
35. 35.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹275 (c) ₹300 (d) ₹250
36. 36.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹115 (b) ₹161 (c) ₹23 (d) ₹138
37. 37.₹396 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹198 (b) ₹36 (c) ₹252 (d) ₹144
38. 38.If 7 kites cost ₹154, how much do 3 kites cost? (a) ₹150 (b) ₹66 (c) ₹88 (d) ₹462
39. 39.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹126 (b) ₹105 (c) ₹147 (d) ₹21
40. 40.If 6 notebooks cost ₹30, how much do 5 notebooks cost? (a) ₹29 (b) ₹150 (c) ₹25 (d) ₹30

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