Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 441 · 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.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹10 (d) ₹15
2. 2.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹32 (d) ₹48
3. 3.If 9 mangoes cost ₹225, how much do 8 mangoes cost? (a) ₹1800 (b) ₹224 (c) ₹225 (d) ₹200
4. 4.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹16 (c) ₹8 (d) ₹24
5. 5.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹30 (d) ₹27
6. 6.If 8 pens cost ₹32, how much do 7 pens cost? (a) ₹31 (b) ₹224 (c) ₹28 (d) ₹32
7. 7.If 9 kites cost ₹153, how much do 10 kites cost? (a) ₹1530 (b) ₹170 (c) ₹154 (d) ₹187
8. 8.If 4 kites cost ₹68, how much do 3 kites cost? (a) ₹51 (b) ₹68 (c) ₹204 (d) ₹67
9. 9.₹396 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹144 (b) ₹198 (c) ₹36 (d) ₹252
10. 10.If 3 pens cost ₹63, how much do 2 pens cost? (a) ₹42 (b) ₹62 (c) ₹126 (d) ₹63
11. 11.If 7 pens cost ₹133, how much do 2 pens cost? (a) ₹128 (b) ₹38 (c) ₹57 (d) ₹266
12. 12.If 4 kites cost ₹16, how much do 6 kites cost? (a) ₹24 (b) ₹28 (c) ₹96 (d) ₹18
13. 13.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 11 days (c) 21 days (d) 19 days
14. 14.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹325 (b) ₹450 (c) ₹200 (d) ₹50
15. 15.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 19 days (d) 11 days
16. 16.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 13 days (d) 20 days
17. 17.If 5 kites cost ₹25, how much do 10 kites cost? (a) ₹55 (b) ₹50 (c) ₹250 (d) ₹30
18. 18.If 4 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹108 (b) ₹35 (c) ₹36 (d) ₹27
19. 19.₹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
20. 20.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 4 days (d) 16 days
21. 21.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹72 (b) ₹56 (c) ₹8 (d) ₹40
22. 22.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 20 days (d) 5 days
23. 23.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹40 (d) ₹20
24. 24.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹190 (b) ₹95 (c) ₹19 (d) ₹171
25. 25.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹24 (b) ₹66 (c) ₹12 (d) ₹108
26. 26.If 4 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹35 (b) ₹29 (c) ₹140 (d) ₹42
27. 27.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹74 (b) ₹333 (c) ₹37 (d) ₹370
28. 28.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 36 days (d) 16 days
29. 29.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
30. 30.If 3 notebooks cost ₹54, how much do 7 notebooks cost? (a) ₹378 (b) ₹126 (c) ₹144 (d) ₹58
31. 31.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 17 days (d) 11 days
32. 32.If 9 pens cost ₹54, how much do 3 pens cost? (a) ₹162 (b) ₹24 (c) ₹18 (d) ₹48
33. 33.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹88 (b) ₹128 (c) ₹48 (d) ₹16
34. 34.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 14 days (d) 11 days
35. 35.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹240 (b) ₹192 (c) ₹48 (d) ₹216
36. 36.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹15 (c) ₹90 (d) ₹75
37. 37.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 20 days (d) 36 days
38. 38.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 1 day (d) 17 days
39. 39.₹231 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹21 (b) ₹168 (c) ₹84 (d) ₹147
40. 40.If 3 pens cost ₹42, how much do 5 pens cost? (a) ₹210 (b) ₹84 (c) ₹70 (d) ₹44

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