Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 290 · 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.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹48 (d) ₹24
2. 2.If 9 kites cost ₹90, how much do 12 kites cost? (a) ₹130 (b) ₹120 (c) ₹93 (d) ₹1080
3. 3.If 9 mangoes cost ₹54, how much do 11 mangoes cost? (a) ₹72 (b) ₹66 (c) ₹594 (d) ₹56
4. 4.If 2 pens cost ₹34, how much do 11 pens cost? (a) ₹187 (b) ₹204 (c) ₹374 (d) ₹43
5. 5.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 3 days
6. 6.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 6 days (d) 5 days
7. 7.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 3 days
8. 8.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹45 (b) ₹55 (c) ₹44 (d) ₹11
9. 9.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 4 days (d) 17 days
10. 10.If 5 pens cost ₹115, how much do 9 pens cost? (a) ₹207 (b) ₹119 (c) ₹1035 (d) ₹230
11. 11.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹8 (b) ₹16 (c) ₹28 (d) ₹40
12. 12.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹59 (d) ₹58
13. 13.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 10 days (d) 24 days
14. 14.If 5 mangoes cost ₹25, how much do 6 mangoes cost? (a) ₹35 (b) ₹150 (c) ₹30 (d) ₹26
15. 15.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 2 days
16. 16.If 2 kites cost ₹26, how much do 12 kites cost? (a) ₹156 (b) ₹36 (c) ₹169 (d) ₹312
17. 17.If 6 notebooks cost ₹132, how much do 3 notebooks cost? (a) ₹66 (b) ₹129 (c) ₹396 (d) ₹88
18. 18.If 5 pens cost ₹55, how much do 9 pens cost? (a) ₹495 (b) ₹59 (c) ₹110 (d) ₹99
19. 19.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹376 (c) ₹235 (d) ₹47
20. 20.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 7 days (d) 25 days
21. 21.If 3 kites cost ₹42, how much do 8 kites cost? (a) ₹336 (b) ₹112 (c) ₹126 (d) ₹47
22. 22.If 6 pens cost ₹102, how much do 9 pens cost? (a) ₹153 (b) ₹105 (c) ₹170 (d) ₹918
23. 23.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹52 (b) ₹40 (c) ₹64 (d) ₹8
24. 24.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹108 (b) ₹54 (c) ₹81 (d) ₹27
25. 25.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 7 days (d) 6 days
26. 26.If 2 notebooks cost ₹14, how much do 9 notebooks cost? (a) ₹63 (b) ₹21 (c) ₹126 (d) ₹70
27. 27.If 7 mangoes cost ₹35, how much do 10 mangoes cost? (a) ₹50 (b) ₹38 (c) ₹55 (d) ₹350
28. 28.If 3 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹55 (b) ₹90 (c) ₹72 (d) ₹216
29. 29.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 6 days (d) 9 days
30. 30.If 3 notebooks cost ₹51, how much do 12 notebooks cost? (a) ₹221 (b) ₹60 (c) ₹612 (d) ₹204
31. 31.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 3 days (d) 11 days
32. 32.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹160 (b) ₹224 (c) ₹288 (d) ₹32
33. 33.If 8 pens cost ₹104, how much do 10 pens cost? (a) ₹1040 (b) ₹130 (c) ₹143 (d) ₹106
34. 34.₹215 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹172 (b) ₹86 (c) ₹129 (d) ₹43
35. 35.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹25 (b) ₹75 (c) ₹100 (d) ₹125
36. 36.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 7 days (d) 15 days
37. 37.If 2 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹252 (b) ₹41 (c) ₹144 (d) ₹126
38. 38.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 3 days (d) 27 days
39. 39.If 6 pens cost ₹138, how much do 3 pens cost? (a) ₹414 (b) ₹92 (c) ₹69 (d) ₹135
40. 40.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 4 days (d) 9 days

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