Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 209 · 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 5 notebooks cost ₹55, how much do 9 notebooks cost? (a) ₹110 (b) ₹59 (c) ₹99 (d) ₹495
2. 2.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹182 (b) ₹78 (c) ₹26 (d) ₹130
3. 3.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹185 (b) ₹37 (c) ₹222 (d) ₹259
4. 4.If 2 notebooks cost ₹40, how much do 4 notebooks cost? (a) ₹160 (b) ₹42 (c) ₹80 (d) ₹100
5. 5.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 9 days (d) 13 days
6. 6.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 19 days (c) 11 days (d) 9 days
7. 7.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 3 days
8. 8.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 28 days (d) 29 days
9. 9.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 29 days (c) 13 days (d) 28 days
10. 10.If 2 pens cost ₹36, how much do 6 pens cost? (a) ₹216 (b) ₹126 (c) ₹108 (d) ₹40
11. 11.If 7 notebooks cost ₹28, how much do 12 notebooks cost? (a) ₹52 (b) ₹33 (c) ₹48 (d) ₹336
12. 12.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹21 (b) ₹25 (c) ₹20 (d) ₹5
13. 13.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 1 day
14. 14.If 9 pens cost ₹117, how much do 3 pens cost? (a) ₹351 (b) ₹52 (c) ₹111 (d) ₹39
15. 15.If 8 notebooks cost ₹152, how much do 5 notebooks cost? (a) ₹149 (b) ₹760 (c) ₹114 (d) ₹95
16. 16.If 9 pens cost ₹207, how much do 6 pens cost? (a) ₹161 (b) ₹138 (c) ₹204 (d) ₹1242
17. 17.If 3 notebooks cost ₹66, how much do 8 notebooks cost? (a) ₹176 (b) ₹198 (c) ₹528 (d) ₹71
18. 18.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
19. 19.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹273 (b) ₹195 (c) ₹117 (d) ₹39
20. 20.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹52 (b) ₹40 (c) ₹64 (d) ₹8
21. 21.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 11 days (d) 12 days
22. 22.If 2 notebooks cost ₹14, how much do 3 notebooks cost? (a) ₹42 (b) ₹15 (c) ₹21 (d) ₹28
23. 23.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 3 days (d) 5 days
24. 24.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹84 (d) ₹63
25. 25.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 43 days (c) 7 days (d) 17 days
26. 26.If 4 mangoes cost ₹40, how much do 12 mangoes cost? (a) ₹130 (b) ₹48 (c) ₹120 (d) ₹480
27. 27.₹133 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹114 (d) ₹95
28. 28.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹105 (b) ₹84 (c) ₹63 (d) ₹21
29. 29.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
30. 30.If 9 notebooks cost ₹171, how much do 2 notebooks cost? (a) ₹164 (b) ₹57 (c) ₹342 (d) ₹38
31. 31.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 10 days (d) 7 days
32. 32.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 27 days (d) 1 day
33. 33.If 3 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹32 (b) ₹28 (c) ₹84 (d) ₹16
34. 34.If 4 notebooks cost ₹76, how much do 8 notebooks cost? (a) ₹171 (b) ₹80 (c) ₹608 (d) ₹152
35. 35.If 6 kites cost ₹42, how much do 10 kites cost? (a) ₹77 (b) ₹46 (c) ₹70 (d) ₹420
36. 36.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹34 (b) ₹272 (c) ₹136 (d) ₹238
37. 37.If 9 kites cost ₹36, how much do 4 kites cost? (a) ₹31 (b) ₹20 (c) ₹16 (d) ₹144
38. 38.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹50 (b) ₹90 (c) ₹70 (d) ₹10
39. 39.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 2 days (d) 3 days
40. 40.If 8 mangoes cost ₹112, how much do 12 mangoes cost? (a) ₹168 (b) ₹182 (c) ₹1344 (d) ₹116

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