Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 401 · 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.₹441 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹343 (b) ₹98 (c) ₹392 (d) ₹49
2. 2.If 9 kites cost ₹162, how much do 4 kites cost? (a) ₹72 (b) ₹157 (c) ₹90 (d) ₹648
3. 3.If 3 kites cost ₹60, how much do 4 kites cost? (a) ₹61 (b) ₹80 (c) ₹100 (d) ₹240
4. 4.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹44 (d) ₹32
5. 5.If 8 notebooks cost ₹64, how much do 5 notebooks cost? (a) ₹61 (b) ₹320 (c) ₹40 (d) ₹48
6. 6.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 19 days
7. 7.₹200 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹200 (b) ₹25 (c) ₹100 (d) ₹175
8. 8.If 3 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹108 (b) ₹28 (c) ₹45 (d) ₹36
9. 9.If 3 notebooks cost ₹45, how much do 7 notebooks cost? (a) ₹120 (b) ₹105 (c) ₹315 (d) ₹49
10. 10.If 2 kites cost ₹32, how much do 4 kites cost? (a) ₹34 (b) ₹64 (c) ₹128 (d) ₹80
11. 11.If 8 pens cost ₹176, how much do 6 pens cost? (a) ₹174 (b) ₹1056 (c) ₹132 (d) ₹154
12. 12.If 9 notebooks cost ₹225, how much do 5 notebooks cost? (a) ₹125 (b) ₹1125 (c) ₹221 (d) ₹150
13. 13.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹128 (d) ₹176
14. 14.If 2 mangoes cost ₹22, how much do 10 mangoes cost? (a) ₹121 (b) ₹30 (c) ₹220 (d) ₹110
15. 15.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹6 (b) ₹36 (c) ₹42 (d) ₹30
16. 16.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹66 (b) ₹132 (c) ₹88 (d) ₹45
17. 17.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹42 (b) ₹14 (c) ₹70 (d) ₹84
18. 18.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹110 (b) ₹66 (c) ₹22 (d) ₹88
19. 19.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹34 (b) ₹153 (c) ₹170 (d) ₹17
20. 20.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 27 days (d) 26 days
21. 21.If 8 pens cost ₹112, how much do 9 pens cost? (a) ₹113 (b) ₹140 (c) ₹126 (d) ₹1008
22. 22.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 13 days (d) 11 days
23. 23.If 7 pens cost ₹21, how much do 5 pens cost? (a) ₹18 (b) ₹19 (c) ₹15 (d) ₹105
24. 24.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 1 day (d) 8 days
25. 25.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 32 days (d) 17 days
26. 26.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 11 days
27. 27.If 7 pens cost ₹42, how much do 9 pens cost? (a) ₹378 (b) ₹44 (c) ₹60 (d) ₹54
28. 28.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹112 (b) ₹91 (c) ₹14 (d) ₹70
29. 29.₹144 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹72 (b) ₹144 (c) ₹96 (d) ₹48
30. 30.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 15 days
31. 31.If 7 notebooks cost ₹119, how much do 8 notebooks cost? (a) ₹136 (b) ₹120 (c) ₹952 (d) ₹153
32. 32.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹152 (b) ₹38 (c) ₹342 (d) ₹247
33. 33.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 45 days (d) 21 days
34. 34.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹50 (d) ₹45
35. 35.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 7 days
36. 36.If 2 pens cost ₹8, how much do 8 pens cost? (a) ₹64 (b) ₹36 (c) ₹32 (d) ₹14
37. 37.If 3 kites cost ₹21, how much do 8 kites cost? (a) ₹56 (b) ₹168 (c) ₹26 (d) ₹63
38. 38.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
39. 39.If 9 kites cost ₹216, how much do 3 kites cost? (a) ₹210 (b) ₹648 (c) ₹96 (d) ₹72
40. 40.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 3 days (d) 15 days

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