Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 314 · 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. 1.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 10 days (d) 4 days
2. 2.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 11 days (d) 15 days
3. 3.If 3 pens cost ₹21, how much do 8 pens cost? (a) ₹63 (b) ₹168 (c) ₹56 (d) ₹26
4. 4.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 27 days (c) 3 days (d) 15 days
5. 5.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 24 days (c) 2 days (d) 25 days
6. 6.If 6 kites cost ₹90, how much do 10 kites cost? (a) ₹165 (b) ₹150 (c) ₹94 (d) ₹900
7. 7.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 1 day
8. 8.If 7 notebooks cost ₹126, how much do 9 notebooks cost? (a) ₹128 (b) ₹180 (c) ₹1134 (d) ₹162
9. 9.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹41 (b) ₹287 (c) ₹369 (d) ₹205
10. 10.If 8 notebooks cost ₹64, how much do 2 notebooks cost? (a) ₹16 (b) ₹128 (c) ₹24 (d) ₹58
11. 11.₹210 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹21 (b) ₹189 (c) ₹210 (d) ₹105
12. 12.If 2 kites cost ₹34, how much do 3 kites cost? (a) ₹102 (b) ₹35 (c) ₹68 (d) ₹51
13. 13.If 5 notebooks cost ₹35, how much do 7 notebooks cost? (a) ₹56 (b) ₹245 (c) ₹49 (d) ₹37
14. 14.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
15. 15.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹55 (b) ₹30 (c) ₹80 (d) ₹10
16. 16.If 3 kites cost ₹24, how much do 5 kites cost? (a) ₹40 (b) ₹120 (c) ₹26 (d) ₹48
17. 17.If 8 pens cost ₹88, how much do 12 pens cost? (a) ₹143 (b) ₹92 (c) ₹1056 (d) ₹132
18. 18.If 2 mangoes cost ₹12, how much do 6 mangoes cost? (a) ₹72 (b) ₹36 (c) ₹42 (d) ₹16
19. 19.If 4 pens cost ₹52, how much do 6 pens cost? (a) ₹54 (b) ₹312 (c) ₹91 (d) ₹78
20. 20.If 2 kites cost ₹18, how much do 6 kites cost? (a) ₹63 (b) ₹22 (c) ₹108 (d) ₹54
21. 21.If 4 pens cost ₹100, how much do 5 pens cost? (a) ₹500 (b) ₹125 (c) ₹101 (d) ₹150
22. 22.₹70 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹49 (b) ₹21 (c) ₹35 (d) ₹7
23. 23.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 11 days (d) 25 days
24. 24.If 4 mangoes cost ₹80, how much do 11 mangoes cost? (a) ₹240 (b) ₹880 (c) ₹220 (d) ₹87
25. 25.₹275 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹25 (b) ₹200 (c) ₹100 (d) ₹175
26. 26.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹232 (d) ₹261
27. 27.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹250 (d) ₹225
28. 28.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 35 days (d) 36 days
29. 29.If 3 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹160 (b) ₹140 (c) ₹64 (d) ₹420
30. 30.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹126 (b) ₹28 (c) ₹14 (d) ₹77
31. 31.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 8 days (d) 2 days
32. 32.If 4 kites cost ₹92, how much do 5 kites cost? (a) ₹460 (b) ₹115 (c) ₹138 (d) ₹93
33. 33.If 6 kites cost ₹138, how much do 3 kites cost? (a) ₹135 (b) ₹414 (c) ₹69 (d) ₹92
34. 34.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹12 (b) ₹54 (c) ₹48 (d) ₹60
35. 35.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 22 days (c) 13 days (d) 21 days
36. 36.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 2 days (d) 3 days
37. 37.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 19 days (d) 12 days
38. 38.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 9 days
39. 39.If 7 pens cost ₹119, how much do 5 pens cost? (a) ₹102 (b) ₹85 (c) ₹117 (d) ₹595
40. 40.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹49 (b) ₹392 (c) ₹441 (d) ₹393

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