Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 854 · 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 ₹28, how much do 10 pens cost? (a) ₹40 (b) ₹31 (c) ₹44 (d) ₹280
2. 2.If 9 notebooks cost ₹135, how much do 10 notebooks cost? (a) ₹165 (b) ₹150 (c) ₹1350 (d) ₹136
3. 3.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 17 days (c) 30 days (d) 13 days
4. 4.₹250 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹25 (b) ₹125 (c) ₹225 (d) ₹250
5. 5.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 12 days (d) 6 days
6. 6.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 4 days (d) 17 days
7. 7.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹414 (b) ₹299 (c) ₹46 (d) ₹184
8. 8.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 8 days
9. 9.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹48 (b) ₹144 (c) ₹168 (d) ₹192
10. 10.If 6 kites cost ₹120, how much do 3 kites cost? (a) ₹360 (b) ₹117 (c) ₹80 (d) ₹60
11. 11.If 7 mangoes cost ₹140, how much do 8 mangoes cost? (a) ₹141 (b) ₹160 (c) ₹180 (d) ₹1120
12. 12.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 1 day
13. 13.₹260 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹260 (b) ₹234 (c) ₹130 (d) ₹26
14. 14.If 7 kites cost ₹161, how much do 3 kites cost? (a) ₹157 (b) ₹92 (c) ₹69 (d) ₹483
15. 15.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹141 (d) ₹94
16. 16.If 3 pens cost ₹42, how much do 9 pens cost? (a) ₹126 (b) ₹378 (c) ₹48 (d) ₹140
17. 17.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 15 days (d) 16 days
18. 18.₹78 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹13 (b) ₹78 (c) ₹65 (d) ₹39
19. 19.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹56 (d) ₹35
20. 20.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 15 days (d) 14 days
21. 21.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹13 (b) ₹27 (c) ₹26 (d) ₹39
22. 22.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 1 day (c) 11 days (d) 3 days
23. 23.If 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹100 (b) ₹720 (c) ₹81 (d) ₹90
24. 24.If 7 kites cost ₹91, how much do 9 kites cost? (a) ₹819 (b) ₹93 (c) ₹117 (d) ₹130
25. 25.If 8 pens cost ₹128, how much do 12 pens cost? (a) ₹208 (b) ₹1536 (c) ₹132 (d) ₹192
26. 26.If 4 pens cost ₹12, how much do 12 pens cost? (a) ₹36 (b) ₹144 (c) ₹39 (d) ₹20
27. 27.₹182 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹130 (d) ₹52
28. 28.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹32 (c) ₹8 (d) ₹24
29. 29.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹238 (b) ₹34 (c) ₹170 (d) ₹102
30. 30.If 3 mangoes cost ₹42, how much do 2 mangoes cost? (a) ₹41 (b) ₹42 (c) ₹28 (d) ₹84
31. 31.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹34 (b) ₹85 (c) ₹102 (d) ₹68
32. 32.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹410 (b) ₹41 (c) ₹205 (d) ₹369
33. 33.If 9 pens cost ₹126, how much do 11 pens cost? (a) ₹128 (b) ₹1386 (c) ₹154 (d) ₹168
34. 34.If 2 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹208 (b) ₹42 (c) ₹192 (d) ₹384
35. 35.If 7 mangoes cost ₹147, how much do 8 mangoes cost? (a) ₹1176 (b) ₹168 (c) ₹189 (d) ₹148
36. 36.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 11 days (d) 16 days
37. 37.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹38 (b) ₹209 (c) ₹304 (d) ₹114
38. 38.If 2 pens cost ₹6, how much do 10 pens cost? (a) ₹33 (b) ₹60 (c) ₹14 (d) ₹30
39. 39.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹204 (b) ₹187 (c) ₹170 (d) ₹34
40. 40.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹27 (d) ₹72

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