Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 157 · 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.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹112 (b) ₹252 (c) ₹28 (d) ₹182
2. 2.If 5 pens cost ₹85, how much do 3 pens cost? (a) ₹255 (b) ₹51 (c) ₹83 (d) ₹68
3. 3.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹12 (c) ₹9 (d) ₹6
4. 4.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹96 (b) ₹108 (c) ₹24 (d) ₹120
5. 5.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 14 days (d) 15 days
6. 6.If 6 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹360 (b) ₹40 (c) ₹60 (d) ₹66
7. 7.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 24 days (c) 6 days (d) 9 days
8. 8.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹152 (d) ₹38
9. 9.If 6 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹126 (b) ₹24 (c) ₹19 (d) ₹21
10. 10.If 2 kites cost ₹6, how much do 12 kites cost? (a) ₹36 (b) ₹72 (c) ₹16 (d) ₹39
11. 11.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹189 (c) ₹168 (d) ₹42
12. 12.If 8 pens cost ₹176, how much do 2 pens cost? (a) ₹44 (b) ₹170 (c) ₹66 (d) ₹352
13. 13.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 16 days (c) 4 days (d) 31 days
14. 14.If 7 mangoes cost ₹21, how much do 5 mangoes cost? (a) ₹19 (b) ₹105 (c) ₹18 (d) ₹15
15. 15.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 8 days
16. 16.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 3 days
17. 17.If 9 mangoes cost ₹99, how much do 2 mangoes cost? (a) ₹33 (b) ₹92 (c) ₹22 (d) ₹198
18. 18.If 7 mangoes cost ₹42, how much do 2 mangoes cost? (a) ₹37 (b) ₹84 (c) ₹12 (d) ₹18
19. 19.If 9 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹12 (b) ₹108 (c) ₹16 (d) ₹30
20. 20.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 11 days
21. 21.If 5 notebooks cost ₹75, how much do 11 notebooks cost? (a) ₹81 (b) ₹825 (c) ₹165 (d) ₹180
22. 22.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹108 (d) ₹144
23. 23.₹234 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹234 (b) ₹117 (c) ₹208 (d) ₹26
24. 24.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹304 (b) ₹266 (c) ₹38 (d) ₹152
25. 25.If 7 notebooks cost ₹133, how much do 12 notebooks cost? (a) ₹247 (b) ₹1596 (c) ₹228 (d) ₹138
26. 26.If 3 pens cost ₹12, how much do 9 pens cost? (a) ₹36 (b) ₹108 (c) ₹40 (d) ₹18
27. 27.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹115 (d) ₹207
28. 28.If 7 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹66 (b) ₹420 (c) ₹60 (d) ₹45
29. 29.If 4 mangoes cost ₹64, how much do 3 mangoes cost? (a) ₹64 (b) ₹192 (c) ₹48 (d) ₹63
30. 30.If 4 kites cost ₹24, how much do 5 kites cost? (a) ₹120 (b) ₹30 (c) ₹36 (d) ₹25
31. 31.If 6 pens cost ₹78, how much do 9 pens cost? (a) ₹702 (b) ₹117 (c) ₹81 (d) ₹130
32. 32.If 7 mangoes cost ₹168, how much do 4 mangoes cost? (a) ₹672 (b) ₹120 (c) ₹96 (d) ₹165
33. 33.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 6 days (d) 7 days
34. 34.If 7 notebooks cost ₹21, how much do 12 notebooks cost? (a) ₹252 (b) ₹39 (c) ₹26 (d) ₹36
35. 35.If 8 mangoes cost ₹176, how much do 11 mangoes cost? (a) ₹1936 (b) ₹242 (c) ₹264 (d) ₹179
36. 36.If 9 kites cost ₹72, how much do 11 kites cost? (a) ₹88 (b) ₹74 (c) ₹96 (d) ₹792
37. 37.If 3 notebooks cost ₹51, how much do 4 notebooks cost? (a) ₹52 (b) ₹68 (c) ₹204 (d) ₹85
38. 38.If 3 kites cost ₹48, how much do 5 kites cost? (a) ₹50 (b) ₹240 (c) ₹80 (d) ₹96
39. 39.If 9 kites cost ₹135, how much do 3 kites cost? (a) ₹60 (b) ₹405 (c) ₹45 (d) ₹129
40. 40.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 5 days (d) 13 days

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