Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 356 · 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. 1.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 4 days (d) 3 days
2. 2.If 7 kites cost ₹70, how much do 5 kites cost? (a) ₹350 (b) ₹50 (c) ₹68 (d) ₹60
3. 3.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹184 (b) ₹92 (c) ₹161 (d) ₹23
4. 4.₹308 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹196 (b) ₹28 (c) ₹154 (d) ₹112
5. 5.If 7 notebooks cost ₹147, how much do 9 notebooks cost? (a) ₹149 (b) ₹210 (c) ₹189 (d) ₹1323
6. 6.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 12 days (d) 11 days
7. 7.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 10 days (d) 9 days
8. 8.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹56 (d) ₹112
9. 9.If 3 pens cost ₹54, how much do 2 pens cost? (a) ₹108 (b) ₹54 (c) ₹36 (d) ₹53
10. 10.9 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
11. 11.If 3 notebooks cost ₹72, how much do 6 notebooks cost? (a) ₹432 (b) ₹168 (c) ₹75 (d) ₹144
12. 12.If 7 mangoes cost ₹28, how much do 11 mangoes cost? (a) ₹308 (b) ₹32 (c) ₹48 (d) ₹44
13. 13.₹104 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹13 (b) ₹104 (c) ₹91 (d) ₹52
14. 14.3 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
15. 15.If 4 pens cost ₹60, how much do 3 pens cost? (a) ₹45 (b) ₹180 (c) ₹59 (d) ₹60
16. 16.₹350 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹105 (d) ₹175
17. 17.If 8 notebooks cost ₹24, how much do 2 notebooks cost? (a) ₹48 (b) ₹18 (c) ₹9 (d) ₹6
18. 18.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹18 (c) ₹90 (d) ₹54
19. 19.If 7 pens cost ₹126, how much do 5 pens cost? (a) ₹124 (b) ₹108 (c) ₹90 (d) ₹630
20. 20.If 8 notebooks cost ₹88, how much do 3 notebooks cost? (a) ₹33 (b) ₹264 (c) ₹83 (d) ₹44
21. 21.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 16 days (d) 10 days
22. 22.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹210 (b) ₹21 (c) ₹189 (d) ₹42
23. 23.If 6 notebooks cost ₹120, how much do 5 notebooks cost? (a) ₹100 (b) ₹600 (c) ₹120 (d) ₹119
24. 24.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 15 days (c) 9 days (d) 8 days
25. 25.If 7 pens cost ₹21, how much do 12 pens cost? (a) ₹39 (b) ₹36 (c) ₹252 (d) ₹26
26. 26.₹225 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹180 (b) ₹45 (c) ₹181 (d) ₹225
27. 27.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 2 days (d) 4 days
28. 28.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 17 days (d) 20 days
29. 29.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 24 days (d) 6 days
30. 30.If 2 pens cost ₹6, how much do 12 pens cost? (a) ₹39 (b) ₹72 (c) ₹16 (d) ₹36
31. 31.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
32. 32.If 9 notebooks cost ₹81, how much do 11 notebooks cost? (a) ₹83 (b) ₹108 (c) ₹99 (d) ₹891
33. 33.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹117 (d) ₹104
34. 34.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 16 days (d) 8 days
35. 35.If 3 kites cost ₹69, how much do 12 kites cost? (a) ₹78 (b) ₹299 (c) ₹276 (d) ₹828
36. 36.If 6 pens cost ₹60, how much do 10 pens cost? (a) ₹100 (b) ₹64 (c) ₹600 (d) ₹110
37. 37.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹301 (b) ₹387 (c) ₹215 (d) ₹43
38. 38.If 8 kites cost ₹88, how much do 2 kites cost? (a) ₹176 (b) ₹82 (c) ₹22 (d) ₹33
39. 39.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 6 days
40. 40.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 36 days (d) 4 days

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad