Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 292 · 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. 1.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 15 days (d) 16 days
2. 2.If 7 kites cost ₹161, how much do 6 kites cost? (a) ₹966 (b) ₹138 (c) ₹160 (d) ₹161
3. 3.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹380 (b) ₹342 (c) ₹38 (d) ₹190
4. 4.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹14 (b) ₹49 (c) ₹56 (d) ₹42
5. 5.If 8 mangoes cost ₹160, how much do 3 mangoes cost? (a) ₹480 (b) ₹155 (c) ₹80 (d) ₹60
6. 6.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 20 days
7. 7.If 4 kites cost ₹28, how much do 5 kites cost? (a) ₹35 (b) ₹29 (c) ₹42 (d) ₹140
8. 8.If 5 notebooks cost ₹20, how much do 11 notebooks cost? (a) ₹26 (b) ₹48 (c) ₹44 (d) ₹220
9. 9.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹114 (b) ₹209 (c) ₹38 (d) ₹304
10. 10.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 3 days
11. 11.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹280 (d) ₹240
12. 12.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹220 (b) ₹308 (c) ₹44 (d) ₹396
13. 13.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹180 (b) ₹150 (c) ₹30 (d) ₹210
14. 14.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹16 (d) ₹20
15. 15.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 1 day (d) 21 days
16. 16.If 2 notebooks cost ₹34, how much do 4 notebooks cost? (a) ₹68 (b) ₹36 (c) ₹85 (d) ₹136
17. 17.If 4 pens cost ₹44, how much do 3 pens cost? (a) ₹44 (b) ₹132 (c) ₹43 (d) ₹33
18. 18.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 7 days (d) 10 days
19. 19.₹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
20. 20.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 15 days (d) 10 days
21. 21.If 6 mangoes cost ₹48, how much do 8 mangoes cost? (a) ₹64 (b) ₹50 (c) ₹384 (d) ₹72
22. 22.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 7 days
23. 23.If 4 pens cost ₹24, how much do 3 pens cost? (a) ₹18 (b) ₹23 (c) ₹72 (d) ₹24
24. 24.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 18 days (c) 8 days (d) 15 days
25. 25.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹99 (b) ₹66 (c) ₹67 (d) ₹33
26. 26.If 2 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹64 (b) ₹22 (c) ₹72 (d) ₹128
27. 27.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 2 days (d) 8 days
28. 28.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 2 days
29. 29.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹57 (d) ₹56
30. 30.If 3 mangoes cost ₹33, how much do 6 mangoes cost? (a) ₹198 (b) ₹36 (c) ₹77 (d) ₹66
31. 31.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
32. 32.If 3 kites cost ₹18, how much do 2 kites cost? (a) ₹17 (b) ₹12 (c) ₹18 (d) ₹36
33. 33.If 9 mangoes cost ₹81, how much do 7 mangoes cost? (a) ₹63 (b) ₹567 (c) ₹72 (d) ₹79
34. 34.If 4 pens cost ₹96, how much do 5 pens cost? (a) ₹120 (b) ₹480 (c) ₹97 (d) ₹144
35. 35.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 3 days
36. 36.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹91 (d) ₹78
37. 37.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹29 (b) ₹35 (c) ₹28 (d) ₹7
38. 38.If 8 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹15 (b) ₹35 (c) ₹20 (d) ₹120
39. 39.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 20 days (c) 21 days (d) 14 days
40. 40.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹345 (b) ₹43 (c) ₹387 (d) ₹344

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