Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 967 · 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.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹156 (c) ₹216 (d) ₹96
2. 2.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 11 days
3. 3.If 7 mangoes cost ₹154, how much do 4 mangoes cost? (a) ₹110 (b) ₹151 (c) ₹616 (d) ₹88
4. 4.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 6 days (d) 4 days
5. 5.₹287 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹247 (b) ₹287 (c) ₹246 (d) ₹41
6. 6.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹26 (b) ₹169 (c) ₹234 (d) ₹104
7. 7.If 9 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹22 (b) ₹15 (c) ₹12 (d) ₹108
8. 8.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 11 days (c) 27 days (d) 15 days
9. 9.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 3 days (d) 2 days
10. 10.7 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) 22 days (d) 5 days
11. 11.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹45 (d) ₹27
12. 12.If 3 mangoes cost ₹48, how much do 11 mangoes cost? (a) ₹528 (b) ₹56 (c) ₹192 (d) ₹176
13. 13.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 11 days (d) 16 days
14. 14.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 4 days (d) 3 days
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) 6 days (c) 7 days (d) 8 days
16. 16.If 9 mangoes cost ₹189, how much do 3 mangoes cost? (a) ₹183 (b) ₹84 (c) ₹63 (d) ₹567
17. 17.If 2 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹144 (b) ₹126 (c) ₹41 (d) ₹252
18. 18.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 3 days (d) 10 days
19. 19.If 2 notebooks cost ₹42, how much do 6 notebooks cost? (a) ₹147 (b) ₹252 (c) ₹126 (d) ₹46
20. 20.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
21. 21.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹105 (b) ₹75 (c) ₹135 (d) ₹15
22. 22.₹114 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹19 (d) ₹57
23. 23.If 8 notebooks cost ₹192, how much do 7 notebooks cost? (a) ₹192 (b) ₹1344 (c) ₹168 (d) ₹191
24. 24.If 4 mangoes cost ₹44, how much do 11 mangoes cost? (a) ₹132 (b) ₹121 (c) ₹51 (d) ₹484
25. 25.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 5 days (d) 20 days
26. 26.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹234 (c) ₹36 (d) ₹324
27. 27.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹86 (d) ₹87
28. 28.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹400 (b) ₹200 (c) ₹360 (d) ₹40
29. 29.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 26 days (c) 27 days (d) 17 days
30. 30.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹40 (d) ₹45
31. 31.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹211 (b) ₹35 (c) ₹210 (d) ₹245
32. 32.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹441 (b) ₹245 (c) ₹392 (d) ₹49
33. 33.If 7 notebooks cost ₹84, how much do 2 notebooks cost? (a) ₹79 (b) ₹36 (c) ₹168 (d) ₹24
34. 34.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹114 (b) ₹19 (c) ₹133 (d) ₹95
35. 35.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 10 days (d) 9 days
36. 36.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹27 (b) ₹243 (c) ₹216 (d) ₹81
37. 37.If 5 mangoes cost ₹35, how much do 2 mangoes cost? (a) ₹32 (b) ₹70 (c) ₹14 (d) ₹21
38. 38.₹470 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹47 (b) ₹423 (c) ₹470 (d) ₹235
39. 39.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 13 days
40. 40.If 4 notebooks cost ₹32, how much do 12 notebooks cost? (a) ₹96 (b) ₹104 (c) ₹384 (d) ₹40

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