Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 29 · 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 mangoes cost ₹24, how much do 12 mangoes cost? (a) ₹288 (b) ₹144 (c) ₹156 (d) ₹34
2. 2.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹162 (d) ₹180
3. 3.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 10 days (d) 2 days
4. 4.If 6 mangoes cost ₹120, how much do 8 mangoes cost? (a) ₹160 (b) ₹122 (c) ₹960 (d) ₹180
5. 5.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 1 day (d) 9 days
6. 6.If 2 kites cost ₹12, how much do 11 kites cost? (a) ₹21 (b) ₹132 (c) ₹72 (d) ₹66
7. 7.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹23 (b) ₹138 (c) ₹115 (d) ₹161
8. 8.If 5 notebooks cost ₹35, how much do 11 notebooks cost? (a) ₹84 (b) ₹41 (c) ₹77 (d) ₹385
9. 9.If 2 pens cost ₹38, how much do 9 pens cost? (a) ₹45 (b) ₹342 (c) ₹190 (d) ₹171
10. 10.If 2 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹120 (b) ₹216 (c) ₹108 (d) ₹31
11. 11.If 6 notebooks cost ₹114, how much do 5 notebooks cost? (a) ₹114 (b) ₹570 (c) ₹95 (d) ₹113
12. 12.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹184 (b) ₹368 (c) ₹46 (d) ₹322
13. 13.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹441 (b) ₹49 (c) ₹245 (d) ₹343
14. 14.If 2 pens cost ₹18, how much do 11 pens cost? (a) ₹27 (b) ₹108 (c) ₹99 (d) ₹198
15. 15.If 5 pens cost ₹105, how much do 12 pens cost? (a) ₹273 (b) ₹1260 (c) ₹112 (d) ₹252
16. 16.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 10 days
17. 17.If 8 notebooks cost ₹184, how much do 11 notebooks cost? (a) ₹2024 (b) ₹187 (c) ₹253 (d) ₹276
18. 18.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 18 days (d) 36 days
19. 19.If 8 pens cost ₹184, how much do 6 pens cost? (a) ₹182 (b) ₹1104 (c) ₹161 (d) ₹138
20. 20.If 9 notebooks cost ₹144, how much do 8 notebooks cost? (a) ₹144 (b) ₹143 (c) ₹128 (d) ₹1152
21. 21.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 6 days (d) 7 days
22. 22.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 8 days (d) 12 days
23. 23.If 6 notebooks cost ₹90, how much do 7 notebooks cost? (a) ₹105 (b) ₹630 (c) ₹91 (d) ₹120
24. 24.If 5 kites cost ₹105, how much do 11 kites cost? (a) ₹111 (b) ₹231 (c) ₹252 (d) ₹1155
25. 25.If 3 kites cost ₹18, how much do 4 kites cost? (a) ₹24 (b) ₹19 (c) ₹30 (d) ₹72
26. 26.If 3 pens cost ₹69, how much do 10 pens cost? (a) ₹230 (b) ₹76 (c) ₹253 (d) ₹690
27. 27.If 4 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹120 (b) ₹35 (c) ₹30 (d) ₹22
28. 28.If 7 mangoes cost ₹140, how much do 11 mangoes cost? (a) ₹144 (b) ₹240 (c) ₹220 (d) ₹1540
29. 29.If 4 pens cost ₹44, how much do 12 pens cost? (a) ₹132 (b) ₹143 (c) ₹52 (d) ₹528
30. 30.If 6 pens cost ₹66, how much do 8 pens cost? (a) ₹99 (b) ₹88 (c) ₹528 (d) ₹68
31. 31.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 12 days (d) 7 days
32. 32.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
33. 33.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹14 (c) ₹98 (d) ₹56
34. 34.If 2 kites cost ₹6, how much do 9 kites cost? (a) ₹54 (b) ₹13 (c) ₹27 (d) ₹30
35. 35.If 4 pens cost ₹52, how much do 2 pens cost? (a) ₹39 (b) ₹50 (c) ₹26 (d) ₹104
36. 36.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹11 (b) ₹55 (c) ₹99 (d) ₹77
37. 37.If 4 mangoes cost ₹16, how much do 12 mangoes cost? (a) ₹52 (b) ₹24 (c) ₹48 (d) ₹192
38. 38.₹414 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹368 (b) ₹207 (c) ₹46 (d) ₹414
39. 39.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 13 days
40. 40.If 4 kites cost ₹48, how much do 6 kites cost? (a) ₹84 (b) ₹50 (c) ₹72 (d) ₹288

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