Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 471 · 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 kites cost ₹42, how much do 9 kites cost? (a) ₹210 (b) ₹49 (c) ₹189 (d) ₹378
2. 2.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 28 days (d) 15 days
3. 3.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
4. 4.If 6 kites cost ₹36, how much do 9 kites cost? (a) ₹324 (b) ₹39 (c) ₹60 (d) ₹54
5. 5.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹56 (d) ₹49
6. 6.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 4 days (d) 16 days
7. 7.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹234 (d) ₹195
8. 8.₹315 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹281 (b) ₹35 (c) ₹315 (d) ₹280
9. 9.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹108 (d) ₹99
10. 10.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹155 (d) ₹124
11. 11.If 9 mangoes cost ₹207, how much do 7 mangoes cost? (a) ₹1449 (b) ₹184 (c) ₹161 (d) ₹205
12. 12.If 9 pens cost ₹45, how much do 3 pens cost? (a) ₹135 (b) ₹39 (c) ₹20 (d) ₹15
13. 13.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 20 days (d) 4 days
14. 14.If 4 mangoes cost ₹24, how much do 9 mangoes cost? (a) ₹54 (b) ₹60 (c) ₹29 (d) ₹216
15. 15.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹60 (d) ₹55
16. 16.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 11 days (c) 19 days (d) 36 days
17. 17.If 6 notebooks cost ₹138, how much do 12 notebooks cost? (a) ₹144 (b) ₹276 (c) ₹299 (d) ₹1656
18. 18.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 14 days (d) 20 days
19. 19.If 4 pens cost ₹20, how much do 10 pens cost? (a) ₹26 (b) ₹50 (c) ₹55 (d) ₹200
20. 20.If 6 mangoes cost ₹132, how much do 3 mangoes cost? (a) ₹66 (b) ₹129 (c) ₹396 (d) ₹88
21. 21.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹26 (b) ₹208 (c) ₹182 (d) ₹104
22. 22.If 2 kites cost ₹14, how much do 6 kites cost? (a) ₹49 (b) ₹42 (c) ₹84 (d) ₹18
23. 23.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 61 days (b) 9 days (c) 21 days (d) 60 days
24. 24.If 7 notebooks cost ₹98, how much do 11 notebooks cost? (a) ₹102 (b) ₹1078 (c) ₹154 (d) ₹168
25. 25.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
26. 26.If 8 notebooks cost ₹112, how much do 12 notebooks cost? (a) ₹116 (b) ₹182 (c) ₹1344 (d) ₹168
27. 27.If 8 notebooks cost ₹168, how much do 11 notebooks cost? (a) ₹1848 (b) ₹171 (c) ₹252 (d) ₹231
28. 28.If 5 notebooks cost ₹30, how much do 12 notebooks cost? (a) ₹37 (b) ₹72 (c) ₹360 (d) ₹78
29. 29.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 11 days (d) 15 days
30. 30.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 19 days (d) 9 days
31. 31.If 2 mangoes cost ₹30, how much do 8 mangoes cost? (a) ₹135 (b) ₹36 (c) ₹240 (d) ₹120
32. 32.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 28 days (d) 7 days
33. 33.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 7 days (d) 9 days
34. 34.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹56 (b) ₹16 (c) ₹48 (d) ₹64
35. 35.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹225 (b) ₹270 (c) ₹315 (d) ₹45
36. 36.If 6 pens cost ₹36, how much do 9 pens cost? (a) ₹39 (b) ₹324 (c) ₹60 (d) ₹54
37. 37.₹189 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹169 (b) ₹189 (c) ₹168 (d) ₹21
38. 38.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹135 (d) ₹180
39. 39.If 6 kites cost ₹48, how much do 7 kites cost? (a) ₹56 (b) ₹64 (c) ₹336 (d) ₹49
40. 40.If 7 kites cost ₹56, how much do 12 kites cost? (a) ₹61 (b) ₹672 (c) ₹96 (d) ₹104

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