Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 161 · 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 4 kites cost ₹68, how much do 12 kites cost? (a) ₹204 (b) ₹816 (c) ₹221 (d) ₹76
2. 2.If 2 notebooks cost ₹10, how much do 6 notebooks cost? (a) ₹14 (b) ₹30 (c) ₹35 (d) ₹60
3. 3.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 12 days (d) 8 days
4. 4.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 6 days (d) 5 days
5. 5.If 3 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹60 (b) ₹37 (c) ₹144 (d) ₹48
6. 6.If 2 mangoes cost ₹16, how much do 10 mangoes cost? (a) ₹24 (b) ₹160 (c) ₹88 (d) ₹80
7. 7.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹30 (d) ₹20
8. 8.If 3 mangoes cost ₹12, how much do 4 mangoes cost? (a) ₹20 (b) ₹48 (c) ₹16 (d) ₹13
9. 9.If 9 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹48 (b) ₹44 (c) ₹38 (d) ₹396
10. 10.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 1 day (d) 4 days
11. 11.If 7 notebooks cost ₹49, how much do 3 notebooks cost? (a) ₹28 (b) ₹147 (c) ₹21 (d) ₹45
12. 12.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 17 days (d) 26 days
13. 13.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 16 days (d) 10 days
14. 14.If 9 kites cost ₹117, how much do 12 kites cost? (a) ₹1404 (b) ₹120 (c) ₹169 (d) ₹156
15. 15.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 2 days (d) 3 days
16. 16.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
17. 17.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 2 days (d) 7 days
18. 18.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 12 days (c) 8 days (d) 5 days
19. 19.If 9 pens cost ₹180, how much do 8 pens cost? (a) ₹160 (b) ₹1440 (c) ₹180 (d) ₹179
20. 20.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹80 (b) ₹112 (c) ₹144 (d) ₹16
21. 21.If 5 notebooks cost ₹60, how much do 10 notebooks cost? (a) ₹65 (b) ₹132 (c) ₹600 (d) ₹120
22. 22.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹27 (c) ₹36 (d) ₹9
23. 23.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 7 days (d) 10 days
24. 24.If 3 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹54 (b) ₹108 (c) ₹36 (d) ₹53
25. 25.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹46 (b) ₹161 (c) ₹23 (d) ₹184
26. 26.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹233 (b) ₹232 (c) ₹261 (d) ₹29
27. 27.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹31 (b) ₹62 (c) ₹217 (d) ₹248
28. 28.If 5 notebooks cost ₹90, how much do 8 notebooks cost? (a) ₹93 (b) ₹144 (c) ₹162 (d) ₹720
29. 29.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 7 days (d) 16 days
30. 30.If 2 mangoes cost ₹36, how much do 6 mangoes cost? (a) ₹40 (b) ₹108 (c) ₹126 (d) ₹216
31. 31.₹210 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹210 (d) ₹105
32. 32.If 5 kites cost ₹105, how much do 10 kites cost? (a) ₹1050 (b) ₹110 (c) ₹231 (d) ₹210
33. 33.If 8 kites cost ₹40, how much do 7 kites cost? (a) ₹35 (b) ₹39 (c) ₹280 (d) ₹40
34. 34.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 28 days (d) 7 days
35. 35.₹104 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹104 (b) ₹91 (c) ₹13 (d) ₹52
36. 36.If 5 kites cost ₹40, how much do 11 kites cost? (a) ₹440 (b) ₹46 (c) ₹96 (d) ₹88
37. 37.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 22 days (d) 11 days
38. 38.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 10 days (d) 3 days
39. 39.If 6 notebooks cost ₹132, how much do 10 notebooks cost? (a) ₹242 (b) ₹220 (c) ₹1320 (d) ₹136
40. 40.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹40 (b) ₹21 (c) ₹30 (d) ₹60

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