Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 891 · 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.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹246 (c) ₹287 (d) ₹41
2. 2.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 6 days (d) 5 days
3. 3.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 22 days (c) 16 days (d) 21 days
4. 4.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
5. 5.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹24 (d) ₹32
6. 6.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 7 days (d) 20 days
7. 7.If 4 pens cost ₹84, how much do 12 pens cost? (a) ₹1008 (b) ₹252 (c) ₹273 (d) ₹92
8. 8.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹24 (d) ₹6
9. 9.6 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) 21 days (d) 22 days
10. 10.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹12 (b) ₹10 (c) ₹36 (d) ₹15
11. 11.If 9 notebooks cost ₹180, how much do 3 notebooks cost? (a) ₹80 (b) ₹174 (c) ₹60 (d) ₹540
12. 12.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 5 days
13. 13.If 3 mangoes cost ₹21, how much do 12 mangoes cost? (a) ₹84 (b) ₹252 (c) ₹91 (d) ₹30
14. 14.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 19 days (c) 12 days (d) 18 days
15. 15.If 3 pens cost ₹18, how much do 8 pens cost? (a) ₹144 (b) ₹48 (c) ₹54 (d) ₹23
16. 16.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹54 (c) ₹27 (d) ₹9
17. 17.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹450 (d) ₹350
18. 18.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 1 day (d) 17 days
19. 19.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 28 days (d) 10 days
20. 20.If 3 mangoes cost ₹57, how much do 7 mangoes cost? (a) ₹61 (b) ₹152 (c) ₹133 (d) ₹399
21. 21.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 27 days (d) 26 days
22. 22.If 7 mangoes cost ₹91, how much do 3 mangoes cost? (a) ₹273 (b) ₹39 (c) ₹52 (d) ₹87
23. 23.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 13 days (d) 11 days
24. 24.If 3 notebooks cost ₹75, how much do 7 notebooks cost? (a) ₹79 (b) ₹525 (c) ₹200 (d) ₹175
25. 25.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 7 days (d) 8 days
26. 26.If 7 notebooks cost ₹175, how much do 8 notebooks cost? (a) ₹176 (b) ₹225 (c) ₹200 (d) ₹1400
27. 27.If 8 kites cost ₹40, how much do 4 kites cost? (a) ₹20 (b) ₹36 (c) ₹160 (d) ₹25
28. 28.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹215 (b) ₹301 (c) ₹43 (d) ₹387
29. 29.If 6 mangoes cost ₹114, how much do 2 mangoes cost? (a) ₹110 (b) ₹228 (c) ₹38 (d) ₹57
30. 30.If 9 kites cost ₹216, how much do 12 kites cost? (a) ₹312 (b) ₹2592 (c) ₹288 (d) ₹219
31. 31.If 7 kites cost ₹126, how much do 5 kites cost? (a) ₹630 (b) ₹90 (c) ₹108 (d) ₹124
32. 32.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 10 days (c) 14 days (d) 2 days
33. 33.If 8 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹24 (b) ₹192 (c) ₹44 (d) ₹30
34. 34.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 60 days (b) 61 days (c) 21 days (d) 9 days
35. 35.If 8 pens cost ₹200, how much do 3 pens cost? (a) ₹75 (b) ₹600 (c) ₹195 (d) ₹100
36. 36.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹235 (b) ₹39 (c) ₹234 (d) ₹273
37. 37.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 10 days (d) 1 day
38. 38.If 8 notebooks cost ₹88, how much do 9 notebooks cost? (a) ₹110 (b) ₹89 (c) ₹99 (d) ₹792
39. 39.If 7 notebooks cost ₹98, how much do 4 notebooks cost? (a) ₹56 (b) ₹70 (c) ₹392 (d) ₹95
40. 40.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 2 days (d) 9 days

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