Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 523 · 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 7 pens cost ₹35, how much do 3 pens cost? (a) ₹20 (b) ₹105 (c) ₹31 (d) ₹15
2. 2.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹165 (b) ₹30 (c) ₹60 (d) ₹270
3. 3.If 9 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹39 (b) ₹48 (c) ₹52 (d) ₹432
4. 4.If 9 pens cost ₹63, how much do 5 pens cost? (a) ₹59 (b) ₹35 (c) ₹315 (d) ₹42
5. 5.If 5 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹36 (b) ₹180 (c) ₹45 (d) ₹44
6. 6.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹184 (d) ₹161
7. 7.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 19 days
8. 8.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹72 (b) ₹120 (c) ₹24 (d) ₹96
9. 9.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 10 days (c) 18 days (d) 7 days
10. 10.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹88 (b) ₹220 (c) ₹154 (d) ₹44
11. 11.If 4 mangoes cost ₹92, how much do 9 mangoes cost? (a) ₹828 (b) ₹207 (c) ₹97 (d) ₹230
12. 12.If 7 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹168 (b) ₹30 (c) ₹39 (d) ₹24
13. 13.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹43 (b) ₹387 (c) ₹129 (d) ₹344
14. 14.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 13 days (d) 12 days
15. 15.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹117 (b) ₹130 (c) ₹26 (d) ₹104
16. 16.If 8 kites cost ₹32, how much do 4 kites cost? (a) ₹16 (b) ₹28 (c) ₹20 (d) ₹128
17. 17.If 7 mangoes cost ₹175, how much do 11 mangoes cost? (a) ₹179 (b) ₹300 (c) ₹275 (d) ₹1925
18. 18.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹18 (b) ₹60 (c) ₹13 (d) ₹15
19. 19.If 6 notebooks cost ₹126, how much do 8 notebooks cost? (a) ₹168 (b) ₹189 (c) ₹1008 (d) ₹128
20. 20.If 6 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹91 (b) ₹48 (c) ₹84 (d) ₹504
21. 21.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 9 days (c) 17 days (d) 27 days
22. 22.If 7 kites cost ₹70, how much do 9 kites cost? (a) ₹100 (b) ₹72 (c) ₹630 (d) ₹90
23. 23.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹240 (b) ₹61 (c) ₹80 (d) ₹100
24. 24.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹25 (b) ₹15 (c) ₹5 (d) ₹35
25. 25.If 5 mangoes cost ₹60, how much do 3 mangoes cost? (a) ₹58 (b) ₹180 (c) ₹48 (d) ₹36
26. 26.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 21 days (b) 4 days (c) 48 days (d) 3 days
27. 27.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹149 (b) ₹37 (c) ₹148 (d) ₹185
28. 28.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 21 days (d) 1 day
29. 29.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹273 (d) ₹312
30. 30.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 28 days (b) 19 days (c) 7 days (d) 9 days
31. 31.If 6 mangoes cost ₹96, how much do 9 mangoes cost? (a) ₹864 (b) ₹160 (c) ₹99 (d) ₹144
32. 32.If 5 notebooks cost ₹115, how much do 6 notebooks cost? (a) ₹161 (b) ₹138 (c) ₹116 (d) ₹690
33. 33.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 20 days (c) 6 days (d) 5 days
34. 34.If 9 notebooks cost ₹27, how much do 8 notebooks cost? (a) ₹26 (b) ₹216 (c) ₹24 (d) ₹27
35. 35.If 4 kites cost ₹40, how much do 3 kites cost? (a) ₹39 (b) ₹40 (c) ₹30 (d) ₹120
36. 36.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 5 days (d) 6 days
37. 37.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 9 days
38. 38.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹217 (d) ₹186
39. 39.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 12 days (d) 15 days
40. 40.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹14 (c) ₹7 (d) ₹49

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