Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 91 · 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 9 kites cost ₹153, how much do 10 kites cost? (a) ₹187 (b) ₹1530 (c) ₹170 (d) ₹154
2. 2.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 4 days (d) 14 days
3. 3.If 8 notebooks cost ₹120, how much do 9 notebooks cost? (a) ₹121 (b) ₹135 (c) ₹1080 (d) ₹150
4. 4.If 7 kites cost ₹63, how much do 10 kites cost? (a) ₹99 (b) ₹66 (c) ₹90 (d) ₹630
5. 5.If 3 pens cost ₹9, how much do 2 pens cost? (a) ₹18 (b) ₹8 (c) ₹9 (d) ₹6
6. 6.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 13 days
7. 7.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 4 days (d) 27 days
8. 8.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 5 days (d) 14 days
9. 9.If 9 pens cost ₹216, how much do 8 pens cost? (a) ₹192 (b) ₹1728 (c) ₹215 (d) ₹216
10. 10.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹72 (d) ₹60
11. 11.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 6 days (d) 5 days
12. 12.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹184 (b) ₹23 (c) ₹161 (d) ₹46
13. 13.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 52 days (d) 53 days
14. 14.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹120 (d) ₹84
15. 15.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹114 (d) ₹76
16. 16.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 18 days (d) 3 days
17. 17.If 3 notebooks cost ₹51, how much do 6 notebooks cost? (a) ₹54 (b) ₹119 (c) ₹102 (d) ₹306
18. 18.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹150 (b) ₹200 (c) ₹175 (d) ₹50
19. 19.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹10 (c) ₹70 (d) ₹50
20. 20.If 7 kites cost ₹161, how much do 12 kites cost? (a) ₹299 (b) ₹276 (c) ₹166 (d) ₹1932
21. 21.If 8 pens cost ₹40, how much do 4 pens cost? (a) ₹25 (b) ₹36 (c) ₹20 (d) ₹160
22. 22.If 9 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹33 (b) ₹30 (c) ₹28 (d) ₹270
23. 23.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹160 (c) ₹32 (d) ₹128
24. 24.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹133 (d) ₹171
25. 25.If 3 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹78 (b) ₹216 (c) ₹240 (d) ₹648
26. 26.If 3 mangoes cost ₹24, how much do 2 mangoes cost? (a) ₹16 (b) ₹24 (c) ₹23 (d) ₹48
27. 27.If 3 pens cost ₹48, how much do 11 pens cost? (a) ₹528 (b) ₹192 (c) ₹56 (d) ₹176
28. 28.If 8 kites cost ₹160, how much do 4 kites cost? (a) ₹156 (b) ₹640 (c) ₹100 (d) ₹80
29. 29.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹276 (b) ₹46 (c) ₹230 (d) ₹138
30. 30.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹94 (b) ₹329 (c) ₹376 (d) ₹47
31. 31.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 11 days
32. 32.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹68 (b) ₹85 (c) ₹17 (d) ₹51
33. 33.If 3 pens cost ₹45, how much do 12 pens cost? (a) ₹540 (b) ₹54 (c) ₹195 (d) ₹180
34. 34.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 43 days (c) 17 days (d) 7 days
35. 35.4 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
36. 36.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 11 days (d) 12 days
37. 37.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹88 (c) ₹44 (d) ₹11
38. 38.If 4 pens cost ₹80, how much do 5 pens cost? (a) ₹81 (b) ₹120 (c) ₹400 (d) ₹100
39. 39.If 8 pens cost ₹88, how much do 5 pens cost? (a) ₹85 (b) ₹66 (c) ₹440 (d) ₹55
40. 40.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹300 (b) ₹250 (c) ₹350 (d) ₹50

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