Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 62 · 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.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹64 (b) ₹104 (c) ₹16 (d) ₹144
2. 2.If 7 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹80 (b) ₹36 (c) ₹48 (d) ₹252
3. 3.If 6 kites cost ₹54, how much do 5 kites cost? (a) ₹53 (b) ₹54 (c) ₹270 (d) ₹45
4. 4.If 3 pens cost ₹51, how much do 12 pens cost? (a) ₹204 (b) ₹221 (c) ₹612 (d) ₹60
5. 5.6 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
6. 6.₹42 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹36 (d) ₹6
7. 7.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 16 days (c) 27 days (d) 10 days
8. 8.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹280 (b) ₹240 (c) ₹40 (d) ₹200
9. 9.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹9 (d) ₹73
10. 10.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹69 (b) ₹115 (c) ₹92 (d) ₹23
11. 11.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 34 days (c) 33 days (d) 15 days
12. 12.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 5 days
13. 13.If 7 kites cost ₹56, how much do 3 kites cost? (a) ₹24 (b) ₹168 (c) ₹32 (d) ₹52
14. 14.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
15. 15.If 8 pens cost ₹56, how much do 4 pens cost? (a) ₹28 (b) ₹35 (c) ₹52 (d) ₹224
16. 16.If 6 kites cost ₹126, how much do 10 kites cost? (a) ₹130 (b) ₹210 (c) ₹1260 (d) ₹231
17. 17.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 12 days (d) 8 days
18. 18.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 6 days
19. 19.If 3 pens cost ₹75, how much do 10 pens cost? (a) ₹82 (b) ₹250 (c) ₹750 (d) ₹275
20. 20.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹150 (b) ₹270 (c) ₹30 (d) ₹300
21. 21.If 4 kites cost ₹20, how much do 5 kites cost? (a) ₹100 (b) ₹21 (c) ₹30 (d) ₹25
22. 22.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 9 days
23. 23.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹64 (b) ₹40 (c) ₹8 (d) ₹52
24. 24.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹80 (c) ₹16 (d) ₹112
25. 25.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 1 day (d) 13 days
26. 26.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹20 (d) ₹15
27. 27.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 22 days (d) 13 days
28. 28.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹9 (b) ₹90 (c) ₹36 (d) ₹81
29. 29.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹145 (d) ₹116
30. 30.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹60 (b) ₹75 (c) ₹15 (d) ₹45
31. 31.₹252 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹126 (b) ₹42 (c) ₹210 (d) ₹252
32. 32.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 39 days (c) 40 days (d) 7 days
33. 33.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹7 (d) ₹57
34. 34.If 4 kites cost ₹16, how much do 11 kites cost? (a) ₹176 (b) ₹48 (c) ₹44 (d) ₹23
35. 35.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹264 (b) ₹33 (c) ₹297 (d) ₹99
36. 36.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 4 days (d) 3 days
37. 37.If 5 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹96 (b) ₹118 (c) ₹72 (d) ₹360
38. 38.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 2 days (d) 8 days
39. 39.If 2 notebooks cost ₹6, how much do 5 notebooks cost? (a) ₹15 (b) ₹18 (c) ₹30 (d) ₹9
40. 40.₹200 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹100 (b) ₹25 (c) ₹200 (d) ₹175

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