Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 843 · 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. 1.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 11 days
2. 2.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹36 (b) ₹216 (c) ₹180 (d) ₹252
3. 3.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹32 (b) ₹40 (c) ₹8 (d) ₹20
4. 4.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹91 (b) ₹14 (c) ₹126 (d) ₹56
5. 5.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹144 (c) ₹264 (d) ₹384
6. 6.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 8 days (c) 42 days (d) 20 days
7. 7.If 4 notebooks cost ₹28, how much do 11 notebooks cost? (a) ₹84 (b) ₹77 (c) ₹35 (d) ₹308
8. 8.If 5 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹720 (b) ₹144 (c) ₹84 (d) ₹160
9. 9.If 9 notebooks cost ₹225, how much do 3 notebooks cost? (a) ₹100 (b) ₹75 (c) ₹219 (d) ₹675
10. 10.If 5 mangoes cost ₹70, how much do 10 mangoes cost? (a) ₹75 (b) ₹700 (c) ₹140 (d) ₹154
11. 11.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹272 (b) ₹136 (c) ₹34 (d) ₹238
12. 12.If 5 notebooks cost ₹80, how much do 11 notebooks cost? (a) ₹86 (b) ₹192 (c) ₹880 (d) ₹176
13. 13.If 8 mangoes cost ₹184, how much do 10 mangoes cost? (a) ₹186 (b) ₹253 (c) ₹1840 (d) ₹230
14. 14.If 6 kites cost ₹42, how much do 5 kites cost? (a) ₹41 (b) ₹35 (c) ₹42 (d) ₹210
15. 15.₹210 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹105 (b) ₹84 (c) ₹126 (d) ₹42
16. 16.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 27 days (c) 3 days (d) 17 days
17. 17.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹392 (d) ₹441
18. 18.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹279 (d) ₹155
19. 19.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹21 (c) ₹43 (d) ₹63
20. 20.If 5 mangoes cost ₹100, how much do 8 mangoes cost? (a) ₹800 (b) ₹103 (c) ₹160 (d) ₹180
21. 21.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 10 days
22. 22.If 9 mangoes cost ₹27, how much do 7 mangoes cost? (a) ₹21 (b) ₹189 (c) ₹24 (d) ₹25
23. 23.If 9 pens cost ₹27, how much do 4 pens cost? (a) ₹108 (b) ₹12 (c) ₹15 (d) ₹22
24. 24.If 7 kites cost ₹112, how much do 3 kites cost? (a) ₹336 (b) ₹108 (c) ₹64 (d) ₹48
25. 25.If 7 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹60 (b) ₹45 (c) ₹252 (d) ₹36
26. 26.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 3 days (d) 11 days
27. 27.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 17 days (d) 16 days
28. 28.If 7 mangoes cost ₹133, how much do 10 mangoes cost? (a) ₹209 (b) ₹136 (c) ₹1330 (d) ₹190
29. 29.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 1 day (d) 7 days
30. 30.If 7 notebooks cost ₹56, how much do 5 notebooks cost? (a) ₹48 (b) ₹54 (c) ₹280 (d) ₹40
31. 31.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹210 (b) ₹60 (c) ₹30 (d) ₹135
32. 32.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹186 (d) ₹124
33. 33.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 9 days (d) 3 days
34. 34.If 2 kites cost ₹6, how much do 3 kites cost? (a) ₹7 (b) ₹12 (c) ₹9 (d) ₹18
35. 35.If 5 pens cost ₹85, how much do 6 pens cost? (a) ₹86 (b) ₹510 (c) ₹119 (d) ₹102
36. 36.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 7 days
37. 37.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹240 (b) ₹30 (c) ₹195 (d) ₹150
38. 38.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹153 (b) ₹17 (c) ₹136 (d) ₹51
39. 39.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹48 (b) ₹120 (c) ₹24 (d) ₹84
40. 40.If 6 notebooks cost ₹102, how much do 9 notebooks cost? (a) ₹105 (b) ₹153 (c) ₹170 (d) ₹918

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