Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 87 · 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 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 4 days (d) 1 day
2. 2.₹156 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹78 (b) ₹156 (c) ₹130 (d) ₹26
3. 3.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 13 days (d) 21 days
4. 4.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹72 (c) ₹120 (d) ₹24
5. 5.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 13 days (c) 7 days (d) 5 days
6. 6.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹249 (d) ₹279
7. 7.If 6 kites cost ₹132, how much do 5 kites cost? (a) ₹132 (b) ₹660 (c) ₹131 (d) ₹110
8. 8.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 20 days (c) 8 days (d) 42 days
9. 9.If 8 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹58 (b) ₹24 (c) ₹128 (d) ₹16
10. 10.If 3 notebooks cost ₹9, how much do 10 notebooks cost? (a) ₹90 (b) ₹30 (c) ₹33 (d) ₹16
11. 11.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹22 (b) ₹77 (c) ₹132 (d) ₹154
12. 12.If 6 pens cost ₹54, how much do 10 pens cost? (a) ₹540 (b) ₹58 (c) ₹90 (d) ₹99
13. 13.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹63 (c) ₹21 (d) ₹43
14. 14.If 7 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹18 (b) ₹12 (c) ₹15 (d) ₹84
15. 15.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 8 days (d) 6 days
16. 16.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 11 days (d) 16 days
17. 17.If 2 pens cost ₹28, how much do 8 pens cost? (a) ₹224 (b) ₹34 (c) ₹112 (d) ₹126
18. 18.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹160 (b) ₹176 (c) ₹32 (d) ₹192
19. 19.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 10 days (d) 2 days
20. 20.If 2 notebooks cost ₹28, how much do 9 notebooks cost? (a) ₹35 (b) ₹252 (c) ₹126 (d) ₹140
21. 21.If 6 mangoes cost ₹84, how much do 2 mangoes cost? (a) ₹42 (b) ₹168 (c) ₹28 (d) ₹80
22. 22.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 45 days (d) 9 days
23. 23.If 9 notebooks cost ₹198, how much do 4 notebooks cost? (a) ₹110 (b) ₹88 (c) ₹792 (d) ₹193
24. 24.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹61 (b) ₹75 (c) ₹15 (d) ₹60
25. 25.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹18 (b) ₹48 (c) ₹6 (d) ₹33
26. 26.₹343 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹294 (d) ₹245
27. 27.9 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
28. 28.If 8 pens cost ₹112, how much do 3 pens cost? (a) ₹56 (b) ₹107 (c) ₹336 (d) ₹42
29. 29.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹306 (b) ₹102 (c) ₹54 (d) ₹119
30. 30.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹30 (b) ₹10 (c) ₹55 (d) ₹80
31. 31.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 14 days (d) 16 days
32. 32.₹77 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹67 (b) ₹77 (c) ₹66 (d) ₹11
33. 33.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 21 days (c) 3 days (d) 48 days
34. 34.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹77 (b) ₹55 (c) ₹11 (d) ₹66
35. 35.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹136 (b) ₹68 (c) ₹119 (d) ₹17
36. 36.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹72 (c) ₹12 (d) ₹66
37. 37.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹126 (c) ₹105 (d) ₹147
38. 38.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 17 days
39. 39.If 2 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹120 (b) ₹24 (c) ₹70 (d) ₹60
40. 40.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 36 days (c) 3 days (d) 15 days

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