Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 46 · 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 6 kites cost ₹90, how much do 8 kites cost? (a) ₹720 (b) ₹120 (c) ₹92 (d) ₹135
2. 2.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 8 days (d) 7 days
3. 3.If 2 pens cost ₹38, how much do 8 pens cost? (a) ₹304 (b) ₹44 (c) ₹171 (d) ₹152
4. 4.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 21 days (d) 9 days
5. 5.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹36 (c) ₹180 (d) ₹324
6. 6.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹240 (b) ₹336 (c) ₹48 (d) ₹432
7. 7.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹217 (d) ₹279
8. 8.If 2 pens cost ₹40, how much do 5 pens cost? (a) ₹100 (b) ₹120 (c) ₹43 (d) ₹200
9. 9.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 2 days (d) 3 days
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) 6 days (c) 8 days (d) 7 days
11. 11.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 4 days (d) 27 days
12. 12.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 8 days (d) 10 days
13. 13.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 12 days (d) 16 days
14. 14.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹235 (d) ₹282
15. 15.If 4 kites cost ₹92, how much do 5 kites cost? (a) ₹93 (b) ₹460 (c) ₹138 (d) ₹115
16. 16.If 3 mangoes cost ₹69, how much do 5 mangoes cost? (a) ₹345 (b) ₹71 (c) ₹115 (d) ₹138
17. 17.If 6 kites cost ₹72, how much do 11 kites cost? (a) ₹144 (b) ₹132 (c) ₹792 (d) ₹77
18. 18.If 4 kites cost ₹96, how much do 10 kites cost? (a) ₹240 (b) ₹264 (c) ₹960 (d) ₹102
19. 19.If 7 mangoes cost ₹175, how much do 4 mangoes cost? (a) ₹172 (b) ₹125 (c) ₹100 (d) ₹700
20. 20.If 3 pens cost ₹27, how much do 12 pens cost? (a) ₹117 (b) ₹324 (c) ₹108 (d) ₹36
21. 21.If 3 mangoes cost ₹21, how much do 5 mangoes cost? (a) ₹23 (b) ₹35 (c) ₹105 (d) ₹42
22. 22.If 8 pens cost ₹72, how much do 2 pens cost? (a) ₹27 (b) ₹144 (c) ₹66 (d) ₹18
23. 23.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 24 days (d) 16 days
24. 24.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 13 days (d) 5 days
25. 25.If 4 mangoes cost ₹88, how much do 10 mangoes cost? (a) ₹242 (b) ₹880 (c) ₹220 (d) ₹94
26. 26.If 9 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹720 (b) ₹73 (c) ₹80 (d) ₹88
27. 27.If 9 pens cost ₹117, how much do 12 pens cost? (a) ₹1404 (b) ₹169 (c) ₹120 (d) ₹156
28. 28.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 35 days (d) 36 days
29. 29.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹301 (b) ₹215 (c) ₹258 (d) ₹43
30. 30.If 9 kites cost ₹216, how much do 10 kites cost? (a) ₹2160 (b) ₹240 (c) ₹264 (d) ₹217
31. 31.If 4 mangoes cost ₹100, how much do 12 mangoes cost? (a) ₹1200 (b) ₹325 (c) ₹108 (d) ₹300
32. 32.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹37 (b) ₹222 (c) ₹259 (d) ₹185
33. 33.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹54 (b) ₹189 (c) ₹27 (d) ₹216
34. 34.If 8 notebooks cost ₹200, how much do 2 notebooks cost? (a) ₹194 (b) ₹400 (c) ₹75 (d) ₹50
35. 35.If 7 pens cost ₹35, how much do 12 pens cost? (a) ₹420 (b) ₹40 (c) ₹65 (d) ₹60
36. 36.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹100 (b) ₹240 (c) ₹61 (d) ₹80
37. 37.If 2 notebooks cost ₹30, how much do 6 notebooks cost? (a) ₹34 (b) ₹180 (c) ₹105 (d) ₹90
38. 38.If 4 pens cost ₹56, how much do 5 pens cost? (a) ₹84 (b) ₹280 (c) ₹57 (d) ₹70
39. 39.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹299 (d) ₹368
40. 40.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 14 days (d) 5 days

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