Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 406 · 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.If 9 kites cost ₹216, how much do 3 kites cost? (a) ₹72 (b) ₹210 (c) ₹96 (d) ₹648
2. 2.If 5 mangoes cost ₹110, how much do 7 mangoes cost? (a) ₹770 (b) ₹154 (c) ₹176 (d) ₹112
3. 3.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹105 (c) ₹84 (d) ₹21
4. 4.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹103 (b) ₹17 (c) ₹119 (d) ₹102
5. 5.₹189 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹54 (d) ₹162
6. 6.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹180 (b) ₹144 (c) ₹108 (d) ₹36
7. 7.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 9 days (d) 8 days
8. 8.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹168 (b) ₹24 (c) ₹27 (d) ₹22
9. 9.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 46 days (b) 45 days (c) 3 days (d) 17 days
10. 10.If 2 notebooks cost ₹10, how much do 8 notebooks cost? (a) ₹16 (b) ₹80 (c) ₹40 (d) ₹45
11. 11.If 3 notebooks cost ₹36, how much do 9 notebooks cost? (a) ₹108 (b) ₹120 (c) ₹324 (d) ₹42
12. 12.If 4 kites cost ₹48, how much do 12 kites cost? (a) ₹144 (b) ₹56 (c) ₹576 (d) ₹156
13. 13.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 4 days (d) 3 days
14. 14.If 2 pens cost ₹36, how much do 3 pens cost? (a) ₹54 (b) ₹72 (c) ₹108 (d) ₹37
15. 15.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 9 days
16. 16.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 28 days (d) 3 days
17. 17.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 10 days
18. 18.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹18 (c) ₹12 (d) ₹24
19. 19.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹94 (d) ₹47
20. 20.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹231 (d) ₹165
21. 21.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 6 days (d) 8 days
22. 22.If 4 pens cost ₹24, how much do 5 pens cost? (a) ₹120 (b) ₹36 (c) ₹30 (d) ₹25
23. 23.If 5 mangoes cost ₹15, how much do 12 mangoes cost? (a) ₹180 (b) ₹36 (c) ₹39 (d) ₹22
24. 24.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 16 days (d) 4 days
25. 25.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 11 days (c) 36 days (d) 17 days
26. 26.If 7 kites cost ₹168, how much do 12 kites cost? (a) ₹2016 (b) ₹312 (c) ₹173 (d) ₹288
27. 27.If 9 pens cost ₹36, how much do 5 pens cost? (a) ₹24 (b) ₹32 (c) ₹180 (d) ₹20
28. 28.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 27 days (d) 28 days
29. 29.If 5 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹21 (b) ₹28 (c) ₹120 (d) ₹24
30. 30.If 9 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹540 (b) ₹55 (c) ₹66 (d) ₹60
31. 31.If 3 pens cost ₹18, how much do 4 pens cost? (a) ₹30 (b) ₹72 (c) ₹19 (d) ₹24
32. 32.If 5 notebooks cost ₹110, how much do 8 notebooks cost? (a) ₹113 (b) ₹176 (c) ₹880 (d) ₹198
33. 33.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 14 days (d) 9 days
34. 34.If 2 kites cost ₹40, how much do 8 kites cost? (a) ₹46 (b) ₹320 (c) ₹180 (d) ₹160
35. 35.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹231 (d) ₹165
36. 36.₹250 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹175 (b) ₹75 (c) ₹125 (d) ₹25
37. 37.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹55 (b) ₹110 (c) ₹22 (d) ₹88
38. 38.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 37 days (d) 3 days
39. 39.If 3 kites cost ₹69, how much do 7 kites cost? (a) ₹73 (b) ₹483 (c) ₹161 (d) ₹184
40. 40.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 32 days (c) 14 days (d) 2 days

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