Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 591 · 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.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹90 (b) ₹150 (c) ₹30 (d) ₹210
2. 2.If 2 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹72 (b) ₹144 (c) ₹38 (d) ₹90
3. 3.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹30 (d) ₹10
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) 5 days (c) 6 days (d) 4 days
5. 5.If 6 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹45 (b) ₹36 (c) ₹216 (d) ₹52
6. 6.If 2 notebooks cost ₹16, how much do 8 notebooks cost? (a) ₹22 (b) ₹72 (c) ₹64 (d) ₹128
7. 7.If 8 notebooks cost ₹168, how much do 11 notebooks cost? (a) ₹252 (b) ₹171 (c) ₹1848 (d) ₹231
8. 8.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 15 days (d) 13 days
9. 9.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 21 days
10. 10.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹141 (b) ₹47 (c) ₹188 (d) ₹235
11. 11.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹160 (d) ₹96
12. 12.₹429 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹33 (b) ₹132 (c) ₹330 (d) ₹297
13. 13.If 7 kites cost ₹70, how much do 2 kites cost? (a) ₹20 (b) ₹140 (c) ₹65 (d) ₹30
14. 14.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹39 (d) ₹57
15. 15.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
16. 16.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 5 days (d) 9 days
17. 17.If 8 mangoes cost ₹168, how much do 7 mangoes cost? (a) ₹167 (b) ₹1176 (c) ₹168 (d) ₹147
18. 18.If 4 mangoes cost ₹32, how much do 2 mangoes cost? (a) ₹64 (b) ₹24 (c) ₹30 (d) ₹16
19. 19.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹207 (d) ₹23
20. 20.If 8 notebooks cost ₹152, how much do 7 notebooks cost? (a) ₹152 (b) ₹151 (c) ₹133 (d) ₹1064
21. 21.If 6 pens cost ₹96, how much do 4 pens cost? (a) ₹80 (b) ₹94 (c) ₹384 (d) ₹64
22. 22.₹273 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹117 (b) ₹156 (c) ₹195 (d) ₹39
23. 23.If 3 notebooks cost ₹27, how much do 8 notebooks cost? (a) ₹72 (b) ₹216 (c) ₹81 (d) ₹32
24. 24.If 6 mangoes cost ₹126, how much do 9 mangoes cost? (a) ₹189 (b) ₹129 (c) ₹210 (d) ₹1134
25. 25.If 5 notebooks cost ₹55, how much do 8 notebooks cost? (a) ₹58 (b) ₹88 (c) ₹99 (d) ₹440
26. 26.If 5 kites cost ₹30, how much do 4 kites cost? (a) ₹30 (b) ₹29 (c) ₹24 (d) ₹120
27. 27.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹24 (d) ₹42
28. 28.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹120 (b) ₹270 (c) ₹195 (d) ₹30
29. 29.If 2 notebooks cost ₹10, how much do 5 notebooks cost? (a) ₹30 (b) ₹50 (c) ₹13 (d) ₹25
30. 30.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 36 days (d) 19 days
31. 31.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 7 days
32. 32.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹350 (d) ₹300
33. 33.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 9 days
34. 34.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹8 (c) ₹40 (d) ₹28
35. 35.If 4 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹83 (b) ₹84 (c) ₹63 (d) ₹252
36. 36.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹38 (b) ₹228 (c) ₹266 (d) ₹190
37. 37.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹45 (d) ₹40
38. 38.If 7 kites cost ₹42, how much do 3 kites cost? (a) ₹38 (b) ₹24 (c) ₹18 (d) ₹126
39. 39.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹6 (b) ₹21 (c) ₹30 (d) ₹12
40. 40.If 2 notebooks cost ₹50, how much do 3 notebooks cost? (a) ₹150 (b) ₹51 (c) ₹100 (d) ₹75

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