Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 869 · 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 8 pens cost ₹48, how much do 4 pens cost? (a) ₹44 (b) ₹24 (c) ₹30 (d) ₹192
2. 2.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 23 days (c) 22 days (d) 15 days
3. 3.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹216 (b) ₹36 (c) ₹252 (d) ₹180
4. 4.If 3 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹160 (b) ₹420 (c) ₹64 (d) ₹140
5. 5.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹63 (d) ₹84
6. 6.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 3 days
7. 7.If 8 mangoes cost ₹88, how much do 2 mangoes cost? (a) ₹33 (b) ₹22 (c) ₹176 (d) ₹82
8. 8.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 5 days (d) 22 days
9. 9.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 13 days (d) 1 day
10. 10.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 7 days (c) 19 days (d) 53 days
11. 11.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 17 days (d) 16 days
12. 12.If 6 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹71 (b) ₹360 (c) ₹72 (d) ₹60
13. 13.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹132 (d) ₹133
14. 14.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹33 (d) ₹36
15. 15.If 2 mangoes cost ₹8, how much do 11 mangoes cost? (a) ₹44 (b) ₹17 (c) ₹48 (d) ₹88
16. 16.If 2 pens cost ₹42, how much do 5 pens cost? (a) ₹126 (b) ₹105 (c) ₹210 (d) ₹45
17. 17.If 3 kites cost ₹57, how much do 2 kites cost? (a) ₹114 (b) ₹38 (c) ₹56 (d) ₹57
18. 18.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 13 days
19. 19.If 9 mangoes cost ₹207, how much do 11 mangoes cost? (a) ₹209 (b) ₹253 (c) ₹276 (d) ₹2277
20. 20.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 10 days (d) 12 days
21. 21.₹288 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹288 (b) ₹144 (c) ₹256 (d) ₹32
22. 22.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹117 (b) ₹273 (c) ₹195 (d) ₹39
23. 23.If 2 mangoes cost ₹14, how much do 4 mangoes cost? (a) ₹16 (b) ₹35 (c) ₹56 (d) ₹28
24. 24.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 10 days (d) 5 days
25. 25.If 2 pens cost ₹48, how much do 7 pens cost? (a) ₹336 (b) ₹192 (c) ₹53 (d) ₹168
26. 26.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
27. 27.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹70 (b) ₹56 (c) ₹14 (d) ₹35
28. 28.If 4 pens cost ₹76, how much do 5 pens cost? (a) ₹114 (b) ₹380 (c) ₹77 (d) ₹95
29. 29.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 10 days (c) 41 days (d) 20 days
30. 30.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 8 days (d) 6 days
31. 31.If 2 pens cost ₹36, how much do 4 pens cost? (a) ₹38 (b) ₹90 (c) ₹72 (d) ₹144
32. 32.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹141 (c) ₹175 (d) ₹140
33. 33.If 3 mangoes cost ₹48, how much do 2 mangoes cost? (a) ₹96 (b) ₹32 (c) ₹48 (d) ₹47
34. 34.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 28 days (c) 27 days (d) 13 days
35. 35.If 6 kites cost ₹30, how much do 7 kites cost? (a) ₹31 (b) ₹210 (c) ₹35 (d) ₹40
36. 36.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹12 (b) ₹66 (c) ₹60 (d) ₹72
37. 37.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹280 (b) ₹140 (c) ₹28 (d) ₹252
38. 38.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹144 (b) ₹264 (c) ₹48 (d) ₹384
39. 39.If 5 mangoes cost ₹55, how much do 8 mangoes cost? (a) ₹99 (b) ₹88 (c) ₹440 (d) ₹58
40. 40.If 2 pens cost ₹38, how much do 8 pens cost? (a) ₹171 (b) ₹304 (c) ₹152 (d) ₹44

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