Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 191 · 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. 1.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 14 days (c) 8 days (d) 15 days
2. 2.If 4 mangoes cost ₹40, how much do 12 mangoes cost? (a) ₹480 (b) ₹48 (c) ₹120 (d) ₹130
3. 3.If 4 notebooks cost ₹16, how much do 5 notebooks cost? (a) ₹20 (b) ₹17 (c) ₹24 (d) ₹80
4. 4.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 32 days (d) 17 days
5. 5.If 4 notebooks cost ₹88, how much do 9 notebooks cost? (a) ₹220 (b) ₹792 (c) ₹198 (d) ₹93
6. 6.If 6 kites cost ₹48, how much do 7 kites cost? (a) ₹49 (b) ₹56 (c) ₹64 (d) ₹336
7. 7.If 2 pens cost ₹32, how much do 9 pens cost? (a) ₹39 (b) ₹144 (c) ₹288 (d) ₹160
8. 8.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹182 (b) ₹28 (c) ₹224 (d) ₹140
9. 9.If 5 notebooks cost ₹125, how much do 3 notebooks cost? (a) ₹375 (b) ₹123 (c) ₹75 (d) ₹100
10. 10.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 6 days (d) 7 days
11. 11.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹243 (d) ₹216
12. 12.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹56 (d) ₹63
13. 13.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹14 (d) ₹98
14. 14.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 7 days
15. 15.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹120 (b) ₹160 (c) ₹40 (d) ₹80
16. 16.₹77 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹66 (d) ₹67
17. 17.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 10 days (c) 18 days (d) 7 days
18. 18.If 3 pens cost ₹45, how much do 11 pens cost? (a) ₹495 (b) ₹165 (c) ₹180 (d) ₹53
19. 19.If 9 pens cost ₹198, how much do 6 pens cost? (a) ₹195 (b) ₹1188 (c) ₹154 (d) ₹132
20. 20.If 6 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹20 (b) ₹22 (c) ₹16 (d) ₹96
21. 21.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 15 days (d) 14 days
22. 22.If 2 pens cost ₹12, how much do 8 pens cost? (a) ₹18 (b) ₹96 (c) ₹48 (d) ₹54
23. 23.If 9 pens cost ₹54, how much do 5 pens cost? (a) ₹50 (b) ₹270 (c) ₹30 (d) ₹36
24. 24.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹81 (d) ₹108
25. 25.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹230 (d) ₹46
26. 26.If 6 kites cost ₹18, how much do 12 kites cost? (a) ₹39 (b) ₹216 (c) ₹24 (d) ₹36
27. 27.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹70 (d) ₹30
28. 28.₹440 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹360 (b) ₹80 (c) ₹220 (d) ₹40
29. 29.If 8 pens cost ₹192, how much do 11 pens cost? (a) ₹195 (b) ₹288 (c) ₹2112 (d) ₹264
30. 30.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹29 (b) ₹116 (c) ₹232 (d) ₹203
31. 31.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹70 (c) ₹10 (d) ₹50
32. 32.If 8 mangoes cost ₹128, how much do 4 mangoes cost? (a) ₹80 (b) ₹512 (c) ₹64 (d) ₹124
33. 33.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 27 days (d) 19 days
34. 34.If 5 kites cost ₹55, how much do 3 kites cost? (a) ₹165 (b) ₹53 (c) ₹33 (d) ₹44
35. 35.If 7 mangoes cost ₹35, how much do 8 mangoes cost? (a) ₹280 (b) ₹45 (c) ₹40 (d) ₹36
36. 36.If 6 notebooks cost ₹138, how much do 11 notebooks cost? (a) ₹143 (b) ₹276 (c) ₹253 (d) ₹1518
37. 37.If 3 kites cost ₹39, how much do 6 kites cost? (a) ₹42 (b) ₹91 (c) ₹234 (d) ₹78
38. 38.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹49 (b) ₹147 (c) ₹98 (d) ₹196
39. 39.If 5 mangoes cost ₹80, how much do 9 mangoes cost? (a) ₹84 (b) ₹720 (c) ₹144 (d) ₹160
40. 40.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹165 (b) ₹99 (c) ₹33 (d) ₹198

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