Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 949 · 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 7 pens cost ₹112, how much do 6 pens cost? (a) ₹111 (b) ₹96 (c) ₹672 (d) ₹112
2. 2.If 8 pens cost ₹64, how much do 7 pens cost? (a) ₹64 (b) ₹448 (c) ₹56 (d) ₹63
3. 3.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 29 days (c) 1 day (d) 28 days
4. 4.If 7 mangoes cost ₹168, how much do 10 mangoes cost? (a) ₹264 (b) ₹240 (c) ₹1680 (d) ₹171
5. 5.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 17 days (c) 32 days (d) 3 days
6. 6.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 8 days
7. 7.If 3 notebooks cost ₹12, how much do 11 notebooks cost? (a) ₹48 (b) ₹44 (c) ₹132 (d) ₹20
8. 8.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 12 days
9. 9.If 6 pens cost ₹138, how much do 7 pens cost? (a) ₹161 (b) ₹139 (c) ₹184 (d) ₹966
10. 10.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 40 days (c) 41 days (d) 10 days
11. 11.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹36 (c) ₹324 (d) ₹180
12. 12.If 2 kites cost ₹38, how much do 7 kites cost? (a) ₹152 (b) ₹133 (c) ₹266 (d) ₹43
13. 13.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹120 (b) ₹105 (c) ₹15 (d) ₹30
14. 14.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹105 (d) ₹147
15. 15.If 9 kites cost ₹198, how much do 11 kites cost? (a) ₹264 (b) ₹200 (c) ₹2178 (d) ₹242
16. 16.If 9 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹28 (b) ₹119 (c) ₹42 (d) ₹252
17. 17.If 7 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹420 (b) ₹45 (c) ₹60 (d) ₹66
18. 18.If 9 kites cost ₹72, how much do 7 kites cost? (a) ₹504 (b) ₹56 (c) ₹70 (d) ₹64
19. 19.If 2 pens cost ₹8, how much do 3 pens cost? (a) ₹9 (b) ₹16 (c) ₹12 (d) ₹24
20. 20.If 7 pens cost ₹175, how much do 9 pens cost? (a) ₹177 (b) ₹225 (c) ₹1575 (d) ₹250
21. 21.₹516 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹215 (b) ₹258 (c) ₹301 (d) ₹43
22. 22.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹64 (b) ₹84 (c) ₹105 (d) ₹252
23. 23.If 7 mangoes cost ₹56, how much do 3 mangoes cost? (a) ₹52 (b) ₹24 (c) ₹32 (d) ₹168
24. 24.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 8 days (d) 12 days
25. 25.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 11 days (d) 8 days
26. 26.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 14 days (d) 20 days
27. 27.If 9 pens cost ₹63, how much do 11 pens cost? (a) ₹693 (b) ₹84 (c) ₹65 (d) ₹77
28. 28.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹18 (d) ₹48
29. 29.If 4 pens cost ₹36, how much do 11 pens cost? (a) ₹43 (b) ₹396 (c) ₹108 (d) ₹99
30. 30.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 12 days (d) 5 days
31. 31.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹99 (b) ₹88 (c) ₹22 (d) ₹110
32. 32.If 7 notebooks cost ₹35, how much do 3 notebooks cost? (a) ₹31 (b) ₹105 (c) ₹15 (d) ₹20
33. 33.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 15 days (c) 13 days (d) 16 days
34. 34.If 2 kites cost ₹38, how much do 10 kites cost? (a) ₹209 (b) ₹190 (c) ₹46 (d) ₹380
35. 35.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 2 days (d) 4 days
36. 36.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹100 (b) ₹75 (c) ₹125 (d) ₹25
37. 37.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹63 (d) ₹56
38. 38.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 10 days (d) 6 days
39. 39.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 5 days
40. 40.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹112 (b) ₹56 (c) ₹96 (d) ₹16

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