Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 159 · 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.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹52 (b) ₹13 (c) ₹65 (d) ₹78
2. 2.If 5 pens cost ₹15, how much do 7 pens cost? (a) ₹24 (b) ₹105 (c) ₹21 (d) ₹17
3. 3.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 20 days (d) 21 days
4. 4.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹86 (b) ₹129 (c) ₹43 (d) ₹87
5. 5.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 4 days (d) 5 days
6. 6.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 16 days (d) 14 days
7. 7.₹66 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹54 (b) ₹12 (c) ₹6 (d) ₹33
8. 8.If 2 mangoes cost ₹12, how much do 4 mangoes cost? (a) ₹14 (b) ₹30 (c) ₹48 (d) ₹24
9. 9.If 6 notebooks cost ₹120, how much do 4 notebooks cost? (a) ₹480 (b) ₹80 (c) ₹118 (d) ₹100
10. 10.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹10 (b) ₹20 (c) ₹5 (d) ₹15
11. 11.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 15 days (c) 6 days (d) 5 days
12. 12.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 1 day
13. 13.If 3 notebooks cost ₹18, how much do 5 notebooks cost? (a) ₹36 (b) ₹20 (c) ₹90 (d) ₹30
14. 14.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹120 (b) ₹100 (c) ₹20 (d) ₹60
15. 15.If 3 mangoes cost ₹75, how much do 10 mangoes cost? (a) ₹275 (b) ₹250 (c) ₹750 (d) ₹82
16. 16.If 2 kites cost ₹38, how much do 11 kites cost? (a) ₹209 (b) ₹228 (c) ₹47 (d) ₹418
17. 17.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 7 days (d) 6 days
18. 18.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹160 (c) ₹32 (d) ₹128
19. 19.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 11 days (d) 15 days
20. 20.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹35 (b) ₹105 (c) ₹140 (d) ₹70
21. 21.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 17 days (d) 32 days
22. 22.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 10 days (d) 4 days
23. 23.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹55 (d) ₹66
24. 24.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹119 (b) ₹17 (c) ₹153 (d) ₹85
25. 25.If 8 mangoes cost ₹184, how much do 7 mangoes cost? (a) ₹184 (b) ₹183 (c) ₹161 (d) ₹1288
26. 26.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 16 days (c) 10 days (d) 26 days
27. 27.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 13 days (d) 11 days
28. 28.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹104 (c) ₹13 (d) ₹117
29. 29.If 3 mangoes cost ₹33, how much do 11 mangoes cost? (a) ₹121 (b) ₹363 (c) ₹132 (d) ₹41
30. 30.If 7 kites cost ₹42, how much do 8 kites cost? (a) ₹336 (b) ₹48 (c) ₹43 (d) ₹54
31. 31.If 9 pens cost ₹117, how much do 10 pens cost? (a) ₹118 (b) ₹1170 (c) ₹130 (d) ₹143
32. 32.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 39 days (d) 7 days
33. 33.If 7 kites cost ₹28, how much do 8 kites cost? (a) ₹29 (b) ₹32 (c) ₹36 (d) ₹224
34. 34.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹147 (d) ₹196
35. 35.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
36. 36.If 2 pens cost ₹24, how much do 11 pens cost? (a) ₹33 (b) ₹132 (c) ₹264 (d) ₹144
37. 37.₹210 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹42 (b) ₹105 (c) ₹126 (d) ₹84
38. 38.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 11 days (d) 13 days
39. 39.If 3 pens cost ₹75, how much do 9 pens cost? (a) ₹250 (b) ₹225 (c) ₹675 (d) ₹81
40. 40.If 9 notebooks cost ₹171, how much do 5 notebooks cost? (a) ₹95 (b) ₹167 (c) ₹114 (d) ₹855

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