Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 173 · 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.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹184 (d) ₹230
2. 2.If 2 pens cost ₹32, how much do 3 pens cost? (a) ₹33 (b) ₹96 (c) ₹64 (d) ₹48
3. 3.If 7 pens cost ₹77, how much do 3 pens cost? (a) ₹33 (b) ₹231 (c) ₹73 (d) ₹44
4. 4.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹140 (b) ₹105 (c) ₹35 (d) ₹175
5. 5.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 2 days (d) 3 days
6. 6.₹264 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹264 (b) ₹33 (c) ₹132 (d) ₹231
7. 7.If 5 pens cost ₹85, how much do 2 pens cost? (a) ₹51 (b) ₹82 (c) ₹34 (d) ₹170
8. 8.₹205 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹164 (b) ₹82 (c) ₹123 (d) ₹41
9. 9.If 3 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹25 (b) ₹40 (c) ₹96 (d) ₹32
10. 10.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 7 days (d) 5 days
11. 11.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹378 (b) ₹42 (c) ₹210 (d) ₹294
12. 12.If 7 notebooks cost ₹49, how much do 6 notebooks cost? (a) ₹294 (b) ₹48 (c) ₹49 (d) ₹42
13. 13.If 3 pens cost ₹18, how much do 6 pens cost? (a) ₹108 (b) ₹36 (c) ₹42 (d) ₹21
14. 14.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹135 (d) ₹108
15. 15.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹184 (d) ₹161
16. 16.If 3 kites cost ₹72, how much do 12 kites cost? (a) ₹864 (b) ₹288 (c) ₹312 (d) ₹81
17. 17.₹429 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹312 (b) ₹117 (c) ₹351 (d) ₹39
18. 18.₹344 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹344 (b) ₹172 (c) ₹301 (d) ₹43
19. 19.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹70 (d) ₹45
20. 20.If 9 notebooks cost ₹117, how much do 8 notebooks cost? (a) ₹104 (b) ₹117 (c) ₹936 (d) ₹116
21. 21.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 4 days (d) 6 days
22. 22.₹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
23. 23.If 9 mangoes cost ₹72, how much do 7 mangoes cost? (a) ₹70 (b) ₹56 (c) ₹504 (d) ₹64
24. 24.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 28 days (d) 16 days
25. 25.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹40 (b) ₹65 (c) ₹90 (d) ₹10
26. 26.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 9 days
27. 27.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹94 (d) ₹47
28. 28.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 27 days (d) 26 days
29. 29.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 9 days (d) 10 days
30. 30.If 3 pens cost ₹33, how much do 10 pens cost? (a) ₹121 (b) ₹40 (c) ₹330 (d) ₹110
31. 31.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 4 days (d) 11 days
32. 32.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹235 (b) ₹141 (c) ₹47 (d) ₹329
33. 33.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹231 (c) ₹198 (d) ₹165
34. 34.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 5 days (d) 22 days
35. 35.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 1 day (c) 28 days (d) 13 days
36. 36.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹29 (b) ₹116 (c) ₹145 (d) ₹87
37. 37.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 13 days
38. 38.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹78 (d) ₹52
39. 39.If 6 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹72 (b) ₹12 (c) ₹18 (d) ₹32
40. 40.₹261 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹232 (b) ₹58 (c) ₹203 (d) ₹29

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