Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 219 · 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 2 pens cost ₹36, how much do 12 pens cost? (a) ₹46 (b) ₹234 (c) ₹432 (d) ₹216
2. 2.If 3 kites cost ₹69, how much do 7 kites cost? (a) ₹483 (b) ₹184 (c) ₹73 (d) ₹161
3. 3.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 1 day (d) 22 days
4. 4.If 3 notebooks cost ₹72, how much do 6 notebooks cost? (a) ₹168 (b) ₹432 (c) ₹75 (d) ₹144
5. 5.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 4 days (d) 3 days
6. 6.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹145 (d) ₹116
7. 7.If 4 mangoes cost ₹28, how much do 6 mangoes cost? (a) ₹168 (b) ₹30 (c) ₹42 (d) ₹49
8. 8.If 3 pens cost ₹45, how much do 7 pens cost? (a) ₹120 (b) ₹315 (c) ₹105 (d) ₹49
9. 9.If 5 pens cost ₹85, how much do 7 pens cost? (a) ₹87 (b) ₹595 (c) ₹119 (d) ₹136
10. 10.If 6 kites cost ₹114, how much do 5 kites cost? (a) ₹95 (b) ₹113 (c) ₹570 (d) ₹114
11. 11.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹165 (b) ₹198 (c) ₹231 (d) ₹33
12. 12.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 14 days (d) 11 days
13. 13.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹217 (d) ₹186
14. 14.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹210 (b) ₹90 (c) ₹150 (d) ₹30
15. 15.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹54 (b) ₹270 (c) ₹243 (d) ₹27
16. 16.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
17. 17.If 8 pens cost ₹200, how much do 10 pens cost? (a) ₹202 (b) ₹250 (c) ₹275 (d) ₹2000
18. 18.If 5 mangoes cost ₹75, how much do 6 mangoes cost? (a) ₹105 (b) ₹76 (c) ₹450 (d) ₹90
19. 19.If 3 mangoes cost ₹60, how much do 4 mangoes cost? (a) ₹100 (b) ₹240 (c) ₹61 (d) ₹80
20. 20.If 8 pens cost ₹72, how much do 9 pens cost? (a) ₹81 (b) ₹90 (c) ₹648 (d) ₹73
21. 21.If 6 mangoes cost ₹108, how much do 4 mangoes cost? (a) ₹106 (b) ₹432 (c) ₹90 (d) ₹72
22. 22.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 18 days (d) 4 days
23. 23.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹49 (b) ₹35 (c) ₹42 (d) ₹7
24. 24.If 9 kites cost ₹72, how much do 2 kites cost? (a) ₹144 (b) ₹24 (c) ₹16 (d) ₹65
25. 25.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 16 days (c) 5 days (d) 4 days
26. 26.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 33 days (c) 7 days (d) 32 days
27. 27.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹25 (d) ₹15
28. 28.If 8 kites cost ₹168, how much do 2 kites cost? (a) ₹162 (b) ₹336 (c) ₹42 (d) ₹63
29. 29.If 3 pens cost ₹12, how much do 9 pens cost? (a) ₹18 (b) ₹40 (c) ₹108 (d) ₹36
30. 30.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 13 days (c) 18 days (d) 3 days
31. 31.If 2 pens cost ₹28, how much do 8 pens cost? (a) ₹112 (b) ₹126 (c) ₹34 (d) ₹224
32. 32.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 10 days (d) 4 days
33. 33.If 2 kites cost ₹34, how much do 11 kites cost? (a) ₹204 (b) ₹43 (c) ₹374 (d) ₹187
34. 34.If 4 mangoes cost ₹88, how much do 12 mangoes cost? (a) ₹1056 (b) ₹96 (c) ₹286 (d) ₹264
35. 35.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹351 (b) ₹195 (c) ₹39 (d) ₹312
36. 36.If 9 pens cost ₹135, how much do 4 pens cost? (a) ₹130 (b) ₹60 (c) ₹75 (d) ₹540
37. 37.If 3 notebooks cost ₹69, how much do 6 notebooks cost? (a) ₹414 (b) ₹72 (c) ₹138 (d) ₹161
38. 38.If 8 notebooks cost ₹48, how much do 6 notebooks cost? (a) ₹42 (b) ₹288 (c) ₹46 (d) ₹36
39. 39.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹210 (b) ₹252 (c) ₹231 (d) ₹42
40. 40.If 3 kites cost ₹27, how much do 4 kites cost? (a) ₹28 (b) ₹108 (c) ₹36 (d) ₹45

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