Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 754 · 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.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹336 (b) ₹144 (c) ₹240 (d) ₹48
2. 2.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹99 (b) ₹162 (c) ₹18 (d) ₹36
3. 3.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹300 (b) ₹50 (c) ₹250 (d) ₹350
4. 4.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹28 (d) ₹21
5. 5.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹52 (d) ₹26
6. 6.If 6 pens cost ₹90, how much do 8 pens cost? (a) ₹92 (b) ₹135 (c) ₹120 (d) ₹720
7. 7.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 3 days
8. 8.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 18 days
9. 9.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹70 (b) ₹350 (c) ₹315 (d) ₹35
10. 10.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 7 days (d) 2 days
11. 11.If 3 kites cost ₹9, how much do 10 kites cost? (a) ₹16 (b) ₹30 (c) ₹33 (d) ₹90
12. 12.If 5 pens cost ₹25, how much do 10 pens cost? (a) ₹55 (b) ₹250 (c) ₹50 (d) ₹30
13. 13.If 5 notebooks cost ₹35, how much do 11 notebooks cost? (a) ₹84 (b) ₹77 (c) ₹41 (d) ₹385
14. 14.₹200 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹200 (b) ₹150 (c) ₹50 (d) ₹100
15. 15.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹171 (b) ₹38 (c) ₹19 (d) ₹190
16. 16.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹21 (d) ₹14
17. 17.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 7 days
18. 18.If 5 pens cost ₹90, how much do 9 pens cost? (a) ₹94 (b) ₹810 (c) ₹180 (d) ₹162
19. 19.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 9 days (d) 14 days
20. 20.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 9 days (d) 8 days
21. 21.If 9 pens cost ₹144, how much do 8 pens cost? (a) ₹144 (b) ₹1152 (c) ₹143 (d) ₹128
22. 22.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 22 days (d) 21 days
23. 23.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹12 (c) ₹6 (d) ₹18
24. 24.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 6 days (d) 5 days
25. 25.If 9 kites cost ₹36, how much do 10 kites cost? (a) ₹360 (b) ₹37 (c) ₹44 (d) ₹40
26. 26.If 7 pens cost ₹49, how much do 9 pens cost? (a) ₹441 (b) ₹70 (c) ₹51 (d) ₹63
27. 27.If 5 notebooks cost ₹115, how much do 12 notebooks cost? (a) ₹1380 (b) ₹122 (c) ₹276 (d) ₹299
28. 28.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹7 (b) ₹21 (c) ₹28 (d) ₹35
29. 29.If 6 kites cost ₹48, how much do 5 kites cost? (a) ₹47 (b) ₹240 (c) ₹48 (d) ₹40
30. 30.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
31. 31.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 18 days (d) 7 days
32. 32.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹56 (b) ₹80 (c) ₹16 (d) ₹32
33. 33.If 5 kites cost ₹25, how much do 9 kites cost? (a) ₹29 (b) ₹50 (c) ₹45 (d) ₹225
34. 34.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 26 days (d) 27 days
35. 35.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 19 days (d) 12 days
36. 36.If 8 mangoes cost ₹72, how much do 3 mangoes cost? (a) ₹36 (b) ₹216 (c) ₹27 (d) ₹67
37. 37.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 13 days (d) 16 days
38. 38.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹324 (b) ₹180 (c) ₹36 (d) ₹252
39. 39.If 7 pens cost ₹168, how much do 5 pens cost? (a) ₹144 (b) ₹840 (c) ₹166 (d) ₹120
40. 40.If 5 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹30 (b) ₹29 (c) ₹24 (d) ₹120

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