Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 524 · 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 ₹24, how much do 10 notebooks cost? (a) ₹31 (b) ₹80 (c) ₹88 (d) ₹240
2. 2.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹60 (c) ₹54 (d) ₹12
3. 3.If 9 mangoes cost ₹63, how much do 10 mangoes cost? (a) ₹630 (b) ₹70 (c) ₹77 (d) ₹64
4. 4.₹92 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹46 (b) ₹69 (c) ₹92 (d) ₹23
5. 5.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹154 (b) ₹28 (c) ₹84 (d) ₹224
6. 6.If 3 notebooks cost ₹21, how much do 11 notebooks cost? (a) ₹77 (b) ₹84 (c) ₹29 (d) ₹231
7. 7.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹276 (b) ₹230 (c) ₹322 (d) ₹46
8. 8.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 10 days (d) 2 days
9. 9.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 9 days (d) 24 days
10. 10.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 33 days (c) 34 days (d) 17 days
11. 11.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 20 days (c) 16 days (d) 5 days
12. 12.If 4 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹45 (b) ₹66 (c) ₹55 (d) ₹220
13. 13.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 15 days (d) 2 days
14. 14.₹550 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹275 (b) ₹450 (c) ₹100 (d) ₹50
15. 15.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 21 days (c) 22 days (d) 12 days
16. 16.If 3 mangoes cost ₹21, how much do 9 mangoes cost? (a) ₹70 (b) ₹63 (c) ₹189 (d) ₹27
17. 17.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹170 (b) ₹272 (c) ₹34 (d) ₹221
18. 18.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days
19. 19.If 2 kites cost ₹16, how much do 6 kites cost? (a) ₹56 (b) ₹48 (c) ₹96 (d) ₹20
20. 20.If 6 pens cost ₹18, how much do 12 pens cost? (a) ₹39 (b) ₹216 (c) ₹36 (d) ₹24
21. 21.₹200 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹150 (d) ₹100
22. 22.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹40 (c) ₹8 (d) ₹32
23. 23.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
24. 24.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 3 days (d) 2 days
25. 25.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹225 (b) ₹45 (c) ₹270 (d) ₹315
26. 26.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹232 (d) ₹203
27. 27.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 26 days (d) 9 days
28. 28.₹322 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹276 (b) ₹161 (c) ₹46 (d) ₹322
29. 29.If 8 kites cost ₹64, how much do 6 kites cost? (a) ₹56 (b) ₹48 (c) ₹62 (d) ₹384
30. 30.If 6 pens cost ₹126, how much do 5 pens cost? (a) ₹125 (b) ₹126 (c) ₹630 (d) ₹105
31. 31.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 44 days (d) 5 days
32. 32.If 9 pens cost ₹162, how much do 5 pens cost? (a) ₹158 (b) ₹108 (c) ₹90 (d) ₹810
33. 33.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
34. 34.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹201 (b) ₹25 (c) ₹200 (d) ₹225
35. 35.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹114 (d) ₹133
36. 36.If 4 notebooks cost ₹24, how much do 6 notebooks cost? (a) ₹36 (b) ₹144 (c) ₹42 (d) ₹26
37. 37.If 2 kites cost ₹44, how much do 4 kites cost? (a) ₹88 (b) ₹46 (c) ₹176 (d) ₹110
38. 38.If 9 kites cost ₹90, how much do 2 kites cost? (a) ₹20 (b) ₹83 (c) ₹30 (d) ₹180
39. 39.If 2 kites cost ₹12, how much do 8 kites cost? (a) ₹96 (b) ₹18 (c) ₹54 (d) ₹48
40. 40.If 2 mangoes cost ₹14, how much do 4 mangoes cost? (a) ₹56 (b) ₹28 (c) ₹16 (d) ₹35

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