Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 521 · 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 3 notebooks cost ₹39, how much do 12 notebooks cost? (a) ₹48 (b) ₹468 (c) ₹169 (d) ₹156
2. 2.If 4 notebooks cost ₹68, how much do 12 notebooks cost? (a) ₹204 (b) ₹76 (c) ₹221 (d) ₹816
3. 3.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹132 (d) ₹165
4. 4.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 17 days (d) 11 days
5. 5.₹186 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹186 (b) ₹155 (c) ₹93 (d) ₹31
6. 6.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹51 (b) ₹85 (c) ₹68 (d) ₹17
7. 7.If 5 pens cost ₹55, how much do 3 pens cost? (a) ₹33 (b) ₹165 (c) ₹44 (d) ₹53
8. 8.If 6 pens cost ₹126, how much do 12 pens cost? (a) ₹1512 (b) ₹273 (c) ₹132 (d) ₹252
9. 9.If 6 kites cost ₹48, how much do 4 kites cost? (a) ₹192 (b) ₹46 (c) ₹40 (d) ₹32
10. 10.If 6 notebooks cost ₹66, how much do 9 notebooks cost? (a) ₹110 (b) ₹594 (c) ₹69 (d) ₹99
11. 11.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹75 (b) ₹125 (c) ₹100 (d) ₹25
12. 12.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 3 days (d) 2 days
13. 13.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹253 (b) ₹46 (c) ₹184 (d) ₹322
14. 14.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 4 days (d) 5 days
15. 15.If 8 notebooks cost ₹120, how much do 9 notebooks cost? (a) ₹1080 (b) ₹121 (c) ₹135 (d) ₹150
16. 16.If 9 kites cost ₹153, how much do 6 kites cost? (a) ₹119 (b) ₹150 (c) ₹918 (d) ₹102
17. 17.If 9 notebooks cost ₹198, how much do 3 notebooks cost? (a) ₹192 (b) ₹66 (c) ₹88 (d) ₹594
18. 18.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 21 days (c) 20 days (d) 11 days
19. 19.If 9 kites cost ₹189, how much do 3 kites cost? (a) ₹567 (b) ₹84 (c) ₹63 (d) ₹183
20. 20.If 7 mangoes cost ₹28, how much do 2 mangoes cost? (a) ₹12 (b) ₹23 (c) ₹56 (d) ₹8
21. 21.If 9 pens cost ₹45, how much do 5 pens cost? (a) ₹30 (b) ₹41 (c) ₹225 (d) ₹25
22. 22.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹31 (b) ₹217 (c) ₹124 (d) ₹248
23. 23.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 9 days (d) 7 days
24. 24.If 9 kites cost ₹54, how much do 8 kites cost? (a) ₹432 (b) ₹54 (c) ₹48 (d) ₹53
25. 25.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹60 (d) ₹30
26. 26.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
27. 27.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 12 days (d) 10 days
28. 28.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 19 days (d) 39 days
29. 29.If 8 pens cost ₹32, how much do 2 pens cost? (a) ₹12 (b) ₹8 (c) ₹64 (d) ₹26
30. 30.If 4 notebooks cost ₹100, how much do 10 notebooks cost? (a) ₹275 (b) ₹1000 (c) ₹250 (d) ₹106
31. 31.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 13 days (d) 11 days
32. 32.If 2 notebooks cost ₹28, how much do 12 notebooks cost? (a) ₹38 (b) ₹182 (c) ₹336 (d) ₹168
33. 33.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 6 days (d) 8 days
34. 34.₹220 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹220 (b) ₹110 (c) ₹22 (d) ₹198
35. 35.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹39 (b) ₹13 (c) ₹117 (d) ₹104
36. 36.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹144 (b) ₹160 (c) ₹16 (d) ₹80
37. 37.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 25 days (c) 16 days (d) 4 days
38. 38.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹287 (b) ₹369 (c) ₹205 (d) ₹41
39. 39.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 17 days (d) 3 days
40. 40.₹222 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹222 (b) ₹111 (c) ₹37 (d) ₹185

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