Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 517 · 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 pens cost ₹26, how much do 9 pens cost? (a) ₹33 (b) ₹117 (c) ₹234 (d) ₹130
2. 2.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 12 days (d) 13 days
3. 3.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹203 (b) ₹87 (c) ₹145 (d) ₹29
4. 4.If 2 kites cost ₹40, how much do 8 kites cost? (a) ₹180 (b) ₹160 (c) ₹46 (d) ₹320
5. 5.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹63 (b) ₹9 (c) ₹27 (d) ₹45
6. 6.If 9 mangoes cost ₹162, how much do 12 mangoes cost? (a) ₹1944 (b) ₹234 (c) ₹216 (d) ₹165
7. 7.If 9 kites cost ₹180, how much do 12 kites cost? (a) ₹2160 (b) ₹240 (c) ₹183 (d) ₹260
8. 8.If 2 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹21 (b) ₹40 (c) ₹30 (d) ₹60
9. 9.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 27 days (d) 28 days
10. 10.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹287 (c) ₹246 (d) ₹41
11. 11.If 5 kites cost ₹95, how much do 2 kites cost? (a) ₹92 (b) ₹38 (c) ₹57 (d) ₹190
12. 12.₹351 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹312 (b) ₹351 (c) ₹313 (d) ₹39
13. 13.If 5 mangoes cost ₹100, how much do 4 mangoes cost? (a) ₹400 (b) ₹99 (c) ₹100 (d) ₹80
14. 14.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 44 days (d) 17 days
15. 15.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹296 (b) ₹333 (c) ₹185 (d) ₹37
16. 16.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹103 (b) ₹119 (c) ₹102 (d) ₹17
17. 17.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹168 (b) ₹84 (c) ₹42 (d) ₹126
18. 18.If 9 notebooks cost ₹198, how much do 3 notebooks cost? (a) ₹66 (b) ₹192 (c) ₹88 (d) ₹594
19. 19.If 5 mangoes cost ₹30, how much do 7 mangoes cost? (a) ₹32 (b) ₹48 (c) ₹42 (d) ₹210
20. 20.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹8 (c) ₹24 (d) ₹32
21. 21.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹60 (b) ₹20 (c) ₹16 (d) ₹25
22. 22.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 28 days (c) 7 days (d) 10 days
23. 23.If 4 notebooks cost ₹40, how much do 10 notebooks cost? (a) ₹46 (b) ₹400 (c) ₹110 (d) ₹100
24. 24.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 22 days (d) 21 days
25. 25.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 12 days (c) 18 days (d) 30 days
26. 26.If 5 kites cost ₹35, how much do 11 kites cost? (a) ₹77 (b) ₹385 (c) ₹84 (d) ₹41
27. 27.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹55 (c) ₹10 (d) ₹20
28. 28.If 4 notebooks cost ₹16, how much do 12 notebooks cost? (a) ₹52 (b) ₹192 (c) ₹24 (d) ₹48
29. 29.If 6 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹72 (b) ₹141 (c) ₹96 (d) ₹432
30. 30.If 5 pens cost ₹105, how much do 7 pens cost? (a) ₹735 (b) ₹107 (c) ₹168 (d) ₹147
31. 31.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹105 (b) ₹63 (c) ₹21 (d) ₹126
32. 32.If 7 pens cost ₹161, how much do 12 pens cost? (a) ₹1932 (b) ₹166 (c) ₹276 (d) ₹299
33. 33.If 7 pens cost ₹98, how much do 2 pens cost? (a) ₹42 (b) ₹196 (c) ₹28 (d) ₹93
34. 34.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 12 days (d) 28 days
35. 35.If 2 kites cost ₹8, how much do 11 kites cost? (a) ₹48 (b) ₹88 (c) ₹17 (d) ₹44
36. 36.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 10 days (c) 2 days (d) 18 days
37. 37.₹180 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹90 (b) ₹135 (c) ₹180 (d) ₹45
38. 38.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹45 (d) ₹25
39. 39.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹128 (b) ₹160 (c) ₹144 (d) ₹32
40. 40.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 19 days (d) 9 days

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